ACI 440.2R-08
Guide for the Design and Construction
of Externally Bonded FRP Systems
for Strengthening Concrete Structures
Reported by ACI Committee 440
First Printing
July 2008
®
American Concrete Institute
Advancing concrete knowledge
Guide for the Design and Construction of Externally Bonded FRP Systems
for Strengthening Concrete Structures
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ISBN 978-0-87031-285-4
ACI 440.2R-08
Guide for the Design and Construction of Externally
Bonded FRP Systems for Strengthening Concrete Structures
Reported by ACI Committee 440
John P. Busel
Chair
Carol K. Shield
Secretary
Tarek Alkhrdaji*
Charles E. Bakis
Lawrence C. Bank
Abdeldjelil Belarbi
Brahim Benmokrane
Russell Gentry
Janos Gergely
William J. Gold
Nabil F. Grace
Mark F. Green
James G. Korff
Michael W. Lee
Maria Lopez de Murphy
Ibrahim M. Mahfouz
Orange S. Marshall
Andrea Prota
Hayder A. Rasheed
Sami H. Rizkalla
Morris Schupack
Rajan Sen
Luke A. Bisby
Gregg J. Blaszak
Timothy E. Bradberry
Gordon L. Brown, Jr.
Vicki L. Brown
Raafat El-Hacha
Garth J. Fallis
Amir Z. Fam
Edward R. Fyfe
Zareh B. Gregorian
Doug D. Gremel
Shawn P. Gross
H. R. Trey Hamilton, III
Issam E. Harik
Kent A. Harries
Mark P. Henderson
Bohdan N. Horeczko
Vistasp M. Karbhari
Amir Mirmiran
Ayman S. Mosallam
John J. Myers
Antonio Nanni
Kenneth Neale
John P. Newhook
Ayman M. Okeil
Carlos E. Ospina
Max L. Porter
Khaled A. Soudki*
Samuel A. Steere, III
Gamil S. Tadros
Jay Thomas
Houssam A. Toutanji
J. Gustavo Tumialan
Milan Vatovec
Stephanie Walkup
David White
*
Co-chairs of the subcommittee that prepared this document.
The Committee also thanks Associate Members Joaquim Barros, Hakim Bouadi, Nestore Galati, Kenneth Neale, Owen Rosenboom, Baolin Wan, in addition to Tom
Harmon, Renata Kotznia, Silvia Rocca, and Subu Subramanien for their contributions.
Fiber-reinforced polymer (FRP) systems for strengthening concrete structures
are an alternative to traditional strengthening techniques, such as steel
plate bonding, section enlargement, and external post-tensioning. FRP
strengthening systems use FRP composite materials as supplemental
externally bonded reinforcement. FRP systems offer advantages over
traditional strengthening techniques: they are lightweight, relatively easy
to install, and are noncorrosive. Due to the characteristics of FRP materials as
well as the behavior of members strengthened with FRP, specific guidance
ACI Committee Reports, Guides, Standard Practices, and
Commentaries are intended for guidance in planning,
designing, executing, and inspecting construction. This
document is intended for the use of individuals who are
competent to evaluate the significance and limitations of its
content and recommendations and who will accept
responsibility for the application of the material it contains.
The American Concrete Institute disclaims any and all
responsibility for the stated principles. The Institute shall not
be liable for any loss or damage arising therefrom.
Reference to this document shall not be made in contract
documents. If items found in this document are desired by the
Architect/Engineer to be a part of the contract documents, they
shall be restated in mandatory language for incorporation by
the Architect/Engineer.
on the use of these systems is needed. This document offers general information on the history and use of FRP strengthening systems; a description
of the unique material properties of FRP; and committee recommendations
on the engineering, construction, and inspection of FRP systems used to
strengthen concrete structures. The proposed guidelines are based on the
knowledge gained from experimental research, analytical work, and field
applications of FRP systems used to strengthen concrete structures.
Keywords: aramid fibers; bridges; buildings; carbon fibers; concrete;
corrosion; crack widths; cracking; cyclic loading; deflection; development
length; earthquake-resistant; fatigue; fiber-reinforced polymers; flexure;
shear; stress; structural analysis; structural design; torsion.
CONTENTS
PART 1—GENERAL
Chapter 1—Introduction and scope, p. 440.2R-3
1.1—Introduction
ACI 440.2R-08 supersedes ACI 440.2R-02 and was adopted and published July 2008.
Copyright © 2008, American Concrete Institute.
All rights reserved including rights of reproduction and use in any form or by any
means, including the making of copies by any photo process, or by electronic or
mechanical device, printed, written, or oral, or recording for sound or visual reproduction
or for use in any knowledge or retrieval system or device, unless permission in writing
is obtained from the copyright proprietors.
440.2R-1
440.2R-2
ACI COMMITTEE REPORT
1.2—Scope and limitations
1.3—Applications and use
1.4—Use of FRP systems
Chapter 2—Notation and definitions, p. 440.2R-5
2.1—Notation
2.2—Definitions and acronyms
Chapter 3—Background information, p. 440.2R-10
3.1—Historical development
3.2—Commercially available externally bonded FRP
systems
PART 2—MATERIALS
Chapter 4—Constituent materials and properties,
p. 440.2R-11
4.1—Constituent materials
4.2—Physical properties
4.3—Mechanical properties
4.4—Time-dependent behavior
4.5—Durability
4.6—FRP systems qualification
PART 3—RECOMMENDED CONSTRUCTION
REQUIREMENTS
Chapter 5—Shipping, storage, and handling,
p. 440.2R-15
5.1—Shipping
5.2—Storage
5.3—Handling
Chapter 6—Installation, p. 440.2R-16
6.1—Contractor competency
6.2—Temperature, humidity, and moisture considerations
6.3—Equipment
6.4—Substrate repair and surface preparation
6.5—Mixing of resins
6.6—Application of FRP systems
6.7—Alignment of FRP materials
6.8—Multiple plies and lap splices
6.9—Curing of resins
6.10—Temporary protection
Chapter 7—Inspection, evaluation, and acceptance,
p. 440.2R-19
7.1—Inspection
7.2—Evaluation and acceptance
Chapter 8—Maintenance and repair, p. 440.2R-21
8.1—General
8.2—Inspection and assessment
8.3—Repair of strengthening system
8.4—Repair of surface coating
PART 4—DESIGN RECOMMENDATIONS
Chapter 9—General design considerations,
p. 440.2R-21
9.1—Design philosophy
9.2—Strengthening limits
9.3—Selection of FRP systems
9.4—Design material properties
Chapter 10—Flexural strengthening, p. 440.2R-24
10.1—Nominal strength
10.2—Reinforced concrete members
10.3—Prestressed concrete members
Chapter 11—Shear strengthening, p. 440.2R-32
11.1—General considerations
11.2—Wrapping schemes
11.3—Nominal shear strength
11.4—FRP contribution to shear strength
Chapter 12—Strengthening of members subjected
to axial force or combined axial and bending
forces, p. 440.2R-34
12.1—Pure axial compression
12.2—Combined axial compression and bending
12.3—Ductility enhancement
12.4—Pure axial tension
Chapter 13—FRP reinforcement details,
p. 440.2R-37
13.1—Bond and delamination
13.2—Detailing of laps and splices
13.3—Bond of near-surface-mounted systems
Chapter 14—Drawings, specifications, and
submittals, p. 440.2R-40
14.1—Engineering requirements
14.2—Drawings and specifications
14.3—Submittals
PART 5—DESIGN EXAMPLES
Chapter 15—Design examples, p. 440.2R-41
15.1—Calculation of FRP system tensile properties
15.2—Comparison of FRP systems’ tensile properties
15.3—Flexural strengthening of an interior reinforced
concrete beam with FRP laminates
15.4—Flexural strengthening of an interior reinforced
concrete beam with NSM FRP bars
15.5—Flexural strengthening of an interior prestressed
concrete beam with FRP laminates
15.6—Shear strengthening of an interior T-beam
15.7—Shear strengthening of an exterior column
15.8—Strengthening of a noncircular concrete column for
axial load increase
15.9—Strengthening of a noncircular concrete column for
increase in axial and bending forces
Chapter 16—References, p. 440.2R-66
16.1—Referenced standards and reports
16.2—Cited references
APPENDIXES
Appendix A—Material properties of carbon, glass,
and aramid fibers, p. 440.2R-72
Appendix B—Summary of standard test methods,
p. 440.2R-73
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Appendix C—Areas of future research, p. 440.2R-74
Appendix D—Methodology for computation of
simplified P-M interaction diagram for noncircular
columns, p. 440.2R-75
PART 1—GENERAL
CHAPTER 1—INTRODUCTION AND SCOPE
1.1—Introduction
The strengthening or retrofitting of existing concrete
structures to resist higher design loads, correct strength loss
due to deterioration, correct design or construction deficiencies,
or increase ductility has traditionally been accomplished
using conventional materials and construction techniques.
Externally bonded steel plates, steel or concrete jackets, and
external post-tensioning are just some of the many traditional
techniques available.
Composite materials made of fibers in a polymeric resin,
also known as fiber-reinforced polymers (FRPs), have
emerged as an alternative to traditional materials for repair and
rehabilitation. For the purposes of this document, an FRP
system is defined as the fibers and resins used to create the
composite laminate, all applicable resins used to bond it to the
concrete substrate, and all applied coatings used to protect the
constituent materials. Coatings used exclusively for aesthetic
reasons are not considered part of an FRP system.
FRP materials are lightweight, noncorrosive, and exhibit
high tensile strength. These materials are readily available in
several forms, ranging from factory-made laminates to dry
fiber sheets that can be wrapped to conform to the geometry
of a structure before adding the polymer resin. The relatively
thin profiles of cured FRP systems are often desirable in
applications where aesthetics or access is a concern.
The growing interest in FRP systems for strengthening and
retrofitting can be attributed to many factors. Although the
fibers and resins used in FRP systems are relatively expensive
compared with traditional strengthening materials such as
concrete and steel, labor and equipment costs to install FRP
systems are often lower (Nanni 1999). FRP systems can also
be used in areas with limited access where traditional
techniques would be difficult to implement.
The basis for this document is the knowledge gained from
a comprehensive review of experimental research, analytical
work, and field applications of FRP strengthening systems.
Areas where further research is needed are highlighted in
this document and compiled in Appendix C.
1.2—Scope and limitations
This document provides guidance for the selection, design,
and installation of FRP systems for externally strengthening
concrete structures. Information on material properties,
design, installation, quality control, and maintenance of FRP
systems used as external reinforcement is presented. This
information can be used to select an FRP system for increasing
the strength and stiffness of reinforced concrete beams or the
ductility of columns and other applications.
A significant body of research serves as the basis for this
document. This research, conducted over the past 25 years,
includes analytical studies, experimental work, and monitored
440.2R-3
field applications of FRP strengthening systems. Based on
the available research, the design procedures outlined in this
document are considered to be conservative. It is important to
specifically point out the areas of the document that still
require research.
The durability and long-term performance of FRP materials
has been the subject of much research; however, this research
remains ongoing. The design guidelines in this document do
account for environmental degradation and long-term
durability by suggesting reduction factors for various
environments. Long-term fatigue and creep are also
addressed by stress limitations indicated in this document.
These factors and limitations are considered conservative. As
more research becomes available, however, these factors will
be modified, and the specific environmental conditions and
loading conditions to which they should apply will be better
defined. Additionally, the coupling effect of environmental
conditions and loading conditions still requires further study.
Caution is advised in applications where the FRP system is
subjected simultaneously to extreme environmental and
stress conditions. The factors associated with the long-term
durability of the FRP system may also affect the tensile
modulus of elasticity of the material used for design.
Many issues regarding bond of the FRP system to the
substrate remain the focus of a great deal of research. For
both flexural and shear strengthening, there are many
different varieties of debonding failure that can govern the
strength of an FRP-strengthened member. While most of the
debonding modes have been identified by researchers, more
accurate methods of predicting debonding are still needed.
Throughout the design procedures, significant limitations on
the strain level achieved in the FRP material (and thus, the
stress level achieved) are imposed to conservatively account
for debonding failure modes. Future development of these
design procedures should include more thorough methods of
predicting debonding.
The document gives guidance on proper detailing and
installation of FRP systems to prevent many types of
debonding failure modes. Steps related to the surface preparation and proper termination of the FRP system are vital in
achieving the levels of strength predicted by the procedures
in this document. Some research has been conducted on
various methods of anchoring FRP strengthening systems
(by mechanical or other means). It is important to recognize,
however, that methods of anchoring these systems are highly
problematic due to the brittle, anisotropic nature of
composite materials. Any proposed method of anchorage
should be heavily scrutinized before field implementation.
The design equations given in this document are the result
of research primarily conducted on moderately sized and
proportioned members. Caution should be given to applications
involving strengthening of very large members or strengthening in disturbed regions (D-regions) of structural members
such as deep beams, corbels, and dapped beam ends. When
warranted, specific limitations on the size of members and
the state of stress are given in this document.
This document applies only to FRP strengthening systems
used as additional tensile reinforcement. It is not recommended
440.2R-4
ACI COMMITTEE REPORT
to use these systems as compressive reinforcement. While
FRP materials can support compressive stresses, there are
numerous issues surrounding the use of FRP for compression.
Microbuckling of fibers can occur if any resin voids are
present in the laminate; laminates themselves can buckle if
not properly adhered or anchored to the substrate, and highly
unreliable compressive strengths result from misaligning
fibers in the field. This document does not address the
construction, quality control, and maintenance issues that
would be involved with the use of the material for this
purpose, nor does it address the design concerns surrounding
such applications. The use of the types of FRP strengthening
systems described in this document to resist compressive
forces is strongly discouraged.
This document does not specifically address masonry
(concrete masonry units, brick, or clay tile) construction,
including masonry walls. Research completed to date,
however, has shown that FRP systems can be used to
strengthen masonry walls, and many of the guidelines
contained in this document may be applicable (Triantafillou
1998b; Ehsani et al. 1997; Marshall et al. 1999).
1.3—Applications and use
FRP systems can be used to rehabilitate or restore the
strength of a deteriorated structural member, retrofit or
strengthen a sound structural member to resist increased
loads due to changes in use of the structure, or address design
or construction errors. The licensed design professional
should determine if an FRP system is a suitable strengthening technique before selecting the type of FRP system.
To assess the suitability of an FRP system for a particular
application, the licensed design professional should perform
a condition assessment of the existing structure that includes
establishing its existing load-carrying capacity, identifying
deficiencies and their causes, and determining the condition
of the concrete substrate. The overall evaluation should
include a thorough field inspection, a review of existing
design or as-built documents, and a structural analysis in
accordance with ACI 364.1R. Existing construction documents
for the structure should be reviewed, including the design
drawings, project specifications, as-built information, field
test reports, past repair documentation, and maintenance
history documentation. The licensed design professional
should conduct a thorough field investigation of the existing
structure in accordance with ACI 437R and other applicable
ACI documents. As a minimum, the field investigation
should determine the following:
• Existing dimensions of the structural members;
• Location, size, and cause of cracks and spalls;
• Location and extent of corrosion of reinforcing steel;
• Presence of active corrosion;
• Quantity and location of existing reinforcing steel;
• In-place compressive strength of concrete; and
• Soundness of the concrete, especially the concrete
cover, in all areas where the FRP system is to be
bonded to the concrete.
The tensile strength of the concrete on surfaces where the
FRP system may be installed should be determined by
conducting a pull-off adhesion test in accordance with ACI
503R. The in-place compressive strength of concrete should
be determined using cores in accordance with ACI 318-05
requirements. The load-carrying capacity of the existing
structure should be based on the information gathered in the
field investigation, the review of design calculations and
drawings, and as determined by analytical methods. Load
tests or other methods can be incorporated into the overall
evaluation process if deemed appropriate.
1.3.1 Strengthening limits—In general, to prevent sudden
failure of the member in case the FRP system is damaged,
strengthening limits are imposed such that the increase in
the load-carrying capacity of a member strengthened with
an FRP system be limited. The philosophy is that a loss of
FRP reinforcement should not cause member failure under
sustained service load. Specific guidance, including load
combinations for assessing member integrity after loss of the
FRP system, is provided in Part 4.
FRP systems used to increase the strength of an existing
member should be designed in accordance with Part 4, which
includes a comprehensive discussion of load limitations,
rational load paths, effects of temperature and environment
on FRP systems, loading considerations, and effects of
reinforcing steel corrosion on FRP system integrity.
1.3.2 Fire and life safety—FRP-strengthened structures
should comply with all applicable building and fire codes.
Smoke generation and flame spread ratings should be satisfied
for the assembly according to applicable building codes
depending on the classification of the building. Smoke and
flame spread ratings should be determined in accordance
with ASTM E84. Coatings (Apicella and Imbrogno 1999)
and insulation systems (Bisby et al. 2005a; Williams et al.
2006) can be used to limit smoke and flame spread.
Because of the degradation of most FRP materials at high
temperature, the strength of externally bonded FRP systems
is assumed to be lost completely in a fire, unless it can be
demonstrated that the FRP temperature remains below its
critical temperature (for example, FRP with a fire-protection
system). The critical temperature of an FRP strengthening
system should be taken as the lowest glass-transition temperature Tg of the components of the repair system, as defined
in Section 1.3.3. The structural member without the FRP
system should possess sufficient strength to resist all
applicable service loads during a fire, as discussed in
Section 9.2.1. The fire endurance of FRP-strengthened
concrete members may be improved through the use of
certain resins, coatings, insulation systems, or other methods of
fire protection (Bisby et al. 2005b). Specific guidance,
including load combinations and a rational approach to
calculating structural fire endurance, is given in Part 4.
1.3.3 Maximum service temperature—The physical and
mechanical properties of the resin components of FRP
systems are influenced by temperature and degrade at
temperatures close to and above their glass-transition
temperature Tg (Bisby et al. 2005b). The Tg for FRP systems
typically ranges from 140 to 180 °F (60 to 82 °C) for existing,
commercially available FRP systems. The Tg for a particular
FRP system can be obtained from the system manufacturer
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
or through testing according to ASTM D4065. The Tg is the
midpoint of the temperature range over which the resin
changes from a glassy state to a viscoelastic state that occurs
over a temperature range of approximately 54 °F (30 °C).
This change in state will degrade the mechanical and bond
properties of the cured laminates. For a dry environment, it is
generally recommended that the anticipated service temperature
of an FRP system not exceed Tg – 27 °F (Tg – 15 °C) (Luo
and Wong 2002; Xian and Karbhari 2007). Further research
is needed to determine the critical service temperature for FRP
systems in other environments. This recommendation is for
elevated service temperatures such as those found in hot
regions or certain industrial environments. The specific case
of fire is described in more detail in Section 9.2.1. In cases
where the FRP will be exposed to a moist environment, the
wet glass-transition temperature Tgw should be used.
1.3.4 Minimum concrete substrate strength—FRP systems
work on sound concrete, and should not be considered for
applications on structural members containing corroded
reinforcing steel or deteriorated concrete unless the substrate
is repaired in accordance with Section 6.4. Concrete distress,
deterioration, and corrosion of existing reinforcing steel
should be evaluated and addressed before the application of
the FRP system. Concrete deterioration concerns include,
but are not limited to, alkali-silica reactions, delayed
ettringite formation, carbonation, longitudinal cracking
around corroded reinforcing steel, and laminar cracking at
the location of the steel reinforcement.
The existing concrete substrate strength is an important
parameter for bond-critical applications, including flexure or
shear strengthening. It should possess the necessary strength
to develop the design stresses of the FRP system through
bond. The substrate, including all bond surfaces between
repaired areas and the original concrete, should have sufficient
direct tensile and shear strength to transfer force to the FRP
system. The tensile strength should be at least 200 psi (1.4 MPa)
as determined by using a pull-off type adhesion test per ICRI
03739. FRP systems should not be used when the concrete
substrate has a compressive strength fc′ less than 2500 psi
(17 MPa). Contact-critical applications, such as column
wrapping for confinement that rely only on intimate contact
between the FRP system and the concrete, are not governed
by this minimum value. Design stresses in the FRP system
are developed by deformation or dilation of the concrete
section in contact-critical applications.
The application of FRP systems will not stop the ongoing
corrosion of existing reinforcing steel (El-Maaddawy et al.
2006). If steel corrosion is evident or is degrading the
concrete substrate, placement of FRP reinforcement is not
recommended without arresting the ongoing corrosion and
repairing any degradation to the substrate.
1.4—Use of FRP systems
This document refers to commercially available FRP
systems consisting of fibers and resins combined in a
specific manner and installed by a specific method. These
systems have been developed through material characterization
and structural testing. Untested combinations of fibers and
440.2R-5
resins could result in an unexpected range of properties as
well as potential material incompatibilities. Any FRP system
considered for use should have sufficient test data
demonstrating adequate performance of the entire system in
similar applications, including its method of installation.
The use of FRP systems developed through material
characterization and structural testing, including welldocumented proprietary systems, is recommended. The use
of untested combinations of fibers and resins should be
avoided. A comprehensive set of test standards for FRP
systems has been developed by several organizations,
including ASTM, ACI, ICRI, and ISIS Canada. Available
standards from these organizations are outlined in Appendix B.
CHAPTER 2—NOTATION AND DEFINITIONS
2.1—Notation
Ac
= cross-sectional area of concrete in compression
member, in.2 (mm2)
Ae
= cross-sectional area of effectively confined
concrete section, in.2 (mm2)
Af
= area of FRP external reinforcement, in.2 (mm2)
Afanchor = area of transverse FRP U-wrap for anchorage of
flexural FRP reinforcement
= area of FRP shear reinforcement with spacing s,
Afv
in.2 (mm2)
Ag
= gross area of concrete section, in.2 (mm2)
Ap
= area of prestressed reinforcement in tension
zone, in.2 (mm2)
As
= area of nonprestressed steel reinforcement, in.2
(mm2)
Asi
= area of i-th layer of longitudinal steel reinforcement, in.2 (mm2)
Ast
= total area of longitudinal reinforcement, in.2
(mm2)
ab
= smaller cross-sectional dimension for rectangular
FRP bars, in. (mm)
b
= width of compression face of member, in. (mm)
= short side dimension of compression member of
prismatic cross section, in. (mm)
bb
= larger cross-sectional dimension for rectangular
FRP bars, in. (mm)
= web width or diameter of circular section, in. (mm)
bw
CE
= environmental reduction factor
c
= distance from extreme compression fiber to the
neutral axis, in. (mm)
D
= diameter of compression member of circular
cross section, in. (mm)
d
= distance from extreme compression fiber to
centroid of tension reinforcement, in. (mm)
df
= effective depth of FRP flexural reinforcement,
in. (mm)
= effective depth of FRP shear reinforcement, in.
dfv
(mm)
= depth of FRP shear reinforcement as shown in
Fig. 11.2, in. (mm)
di
= distance from centroid of i-th layer of longitudinal
steel reinforcement to geometric centroid of
cross section, in. (mm)
440.2R-6
dp
E2
Ec
Ef
Eps
Es
es
em
fc
fc′
f c′
f c′
fcc
′
′
fco
fc,s
ff
ffd
ffe
ff,s
ffu
ffu*
fl
fps
fps,s
fpu
fs
fsi
fs,s
fy
h
ACI COMMITTEE REPORT
= distance from extreme compression fiber to
centroid of prestressed reinforcement, in. (mm)
= diagonal distance of prismatic cross section
(diameter of equivalent circular column), in.
2
2
(mm) = b + h
= slope of linear portion of stress-strain model for
FRP-confined concrete, psi (MPa)
= modulus of elasticity of concrete, psi (MPa)
= tensile modulus of elasticity of FRP, psi (MPa)
= modulus of elasticity of prestressing steel, psi (MPa)
= modulus of elasticity of steel, psi (MPa)
= eccentricity of prestressing steel with respect to
centroidal axis of member at support, in. (mm)
= eccentricity of prestressing steel with respect to
centroidal axis of member at midspan, in. (mm)
= compressive stress in concrete, psi (MPa)
= specified compressive strength of concrete, psi
(MPa)
= mean ultimate tensile strength of FRP based on
a population of 20 or more tensile tests per
ASTM D3039, psi (MPa)
= square root of specified compressive strength of
concrete
= compressive strength of confined concrete, psi
(MPa)
= compressive strength of unconfined concrete;
also equal to 0.85fc′ , psi (MPa)
= compressive stress in concrete at service condition,
psi (MPa)
= stress level in FRP reinforcement, psi (MPa)
= design stress of externally bonded FRP reinforcement, psi (MPa)
= effective stress in the FRP; stress level attained
at section failure, psi (MPa)
= stress level in FRP caused by a moment within
elastic range of member, psi (MPa)
= design ultimate tensile strength of FRP, psi
(MPa)
= ultimate tensile strength of the FRP material as
reported by the manufacturer, psi (MPa)
= maximum confining pressure due to FRP jacket,
psi (MPa)
= stress in prestressed reinforcement at nominal
strength, psi (MPa)
= stress in prestressed reinforcement at service
load, psi (MPa)
= specified tensile strength of prestressing
tendons, psi (MPa)
= stress in nonprestressed steel reinforcement, psi
(MPa)
= stress in the i-th layer of longitudinal steel
reinforcement, psi (MPa)
= stress level in nonprestressed steel reinforcement at service loads, psi (MPa)
= specified yield strength of nonprestressed steel
reinforcement, psi (MPa)
= overall thickness or height of a member, in. (mm)
hf
Icr
Itr
k
k1
k2
kf
Le
ldb
ldf
Mcr
Mn
Mnf
Mnp
Mns
Ms
Msnet
Mu
n
nf
ns
Pe
Pn
p fu
*
pfu
Rn
Rnφ
r
rc
SDL
SLL
Tg
Tgw
Tps
tf
= long side cross-sectional dimension of rectangular compression member, in. (mm)
= member flange thickness, in. (mm)
= moment of inertia of cracked section transformed to concrete, in.4 (mm4)
= moment of inertia of uncracked section transformed to concrete, in.4 (mm4)
= ratio of depth of neutral axis to reinforcement
depth measured from extreme compression fiber
= modification factor applied to κv to account for
concrete strength
= modification factor applied to κv to account for
wrapping scheme
= stiffness per unit width per ply of the FRP
reinforcement, lb/in. (N/mm); kf = Ef tf
= active bond length of FRP laminate, in. (mm)
= development length of near-surface-mounted
(NSM) FRP bar, in. (mm)
= development length of FRP system, in. (mm)
= cracking moment, in.-lb (N-mm)
= nominal flexural strength, in.-lb (N-mm)
= contribution of FRP reinforcement to nominal
flexural strength, lb-in. (N-mm)
= contribution of prestressing reinforcement to
nominal flexural strength, lb-in. (N-mm)
= contribution of steel reinforcement to nominal
flexural strength, lb-in. (N-mm)
= service moment at section, in.-lb (N-mm)
= service moment at section beyond decompression,
in.-lb (N-mm)
= factored moment at a section, in.-lb (N-mm)
= number of plies of FRP reinforcement
= modular ratio of elasticity between FRP and
concrete = Ef /Ec
= modular ratio of elasticity between steel and
concrete = Es /Ec
= effective force in prestressing reinforcement
(after allowance for all prestress losses), lb (N)
= nominal axial compressive strength of a concrete
section, lb (N)
= mean tensile strength per unit width per ply of
FRP reinforcement, lb/in. (N/mm)
= ultimate tensile strength per unit width per ply of
*
FRP reinforcement, lb/in. (N/mm); pfu
=ffu* tf
= nominal strength of a member
= nominal strength of a member subjected to
elevated temperatures associated with a fire
= radius of gyration of a section, in. (mm)
= radius of edges of a prismatic cross section
confined with FRP, in. (mm)
= dead load effects
= live load effects
= glass-transition temperature, °F (°C)
= wet glass-transition temperature, °F (°C)
= tensile force in prestressing steel, lb (N)
= nominal thickness of one ply of FRP reinforcement, in. (mm)
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Vc
Vf
Vn
Vs
wf
yb
yt
α1
αL
αT
β1
εb
εbi
εc
εc′
εccu
εc,s
εct
εcu
εf
εfd
εfe
εfu
ε fu
= nominal shear strength provided by concrete
with steel flexural reinforcement, lb (N)
= nominal shear strength provided by FRP stirrups,
lb (N)
= nominal shear strength, lb (N)
= nominal shear strength provided by steel stirrups,
lb (N)
= width of FRP reinforcing plies, in. (mm)
= distance from centroidal axis of gross section,
neglecting reinforcement, to extreme bottom
fiber, in./in. (mm/mm)
= vertical coordinate within compression region
measured from neutral axis position. It corresponds to transition strain εt′ , in. (mm)
= multiplier on fc′ to determine intensity of an equivalent rectangular stress distribution for concrete
= longitudinal coefficient of thermal expansion,
in./in./°F (mm/mm/°C)
= transverse coefficient of thermal expansion,
in./in./°F (mm/mm/°C)
= ratio of depth of equivalent rectangular stress
block to depth of the neutral axis
= strain level in concrete substrate developed by a
given bending moment (tension is positive), in./in.
(mm/mm)
= strain level in concrete substrate at time of FRP
installation (tension is positive), in./in. (mm/mm)
= strain level in concrete, in./in. (mm/mm)
= maximum strain of unconfined concrete corresponding to fc′ , in./in. (mm/mm); may be taken
as 0.002
= ultimate axial compressive strain of confined
concrete corresponding to 0.85fcc′ in a lightly
confined member (member confined to restore
its concrete design compressive strength), or
ultimate axial compressive strain of confined
concrete corresponding to failure in a heavily
confined member (Fig. 12.1)
= strain level in concrete at service, in./in. (mm/mm)
= concrete tensile strain at level of tensile force
resultant in post-tensioned flexural members,
in./in. (mm/mm)
= ultimate axial strain of unconfined concrete
corresponding to 0.85fco
′ or maximum usable
strain of unconfined concrete, in./in. (mm/mm),
which can occur at 0.85fc′ or 0.003, depending
on the obtained stress-strain curve
= strain level in the FRP reinforcement, in./in.
(mm/ mm)
= debonding strain of externally bonded FRP
reinforcement, in./in. (mm/mm)
= effective strain level in FRP reinforcement
attained at failure, in./in. (mm/mm)
= design rupture strain of FRP reinforcement, in./in.
(mm/mm)
= mean rupture strain of FRP reinforcement based
on a population of 20 or more tensile tests per
ASTM D3039, in./in. (mm/mm)
∗
εfu
εpe
εpi
εpnet
εpnet,s
εps
εps,s
εs
εsy
εt
εt′
φ
κa
κb
κv
κε
ρf
ρg
ρs
σ
τb
ψf
440.2R-7
= ultimate rupture strain of FRP reinforcement,
in./in. (mm/mm)
= effective strain in prestressing steel after losses,
in./in. (mm/mm)
= initial strain level in prestressed steel reinforcement, in./in. (mm/mm)
= net strain in flexural prestressing steel at limit
state after prestress force is discounted (excluding
strains due to effective prestress force after
losses), in./in. (mm/mm)
= net strain in prestressing steel beyond decompression at service, in./in. (mm/mm)
= strain in prestressed reinforcement at nominal
strength, in./in. (mm/mm)
= strain in prestressing steel at service load, in./in.
(mm/mm)
= strain level in nonprestessed steel reinforcement,
in./in. (mm/mm)
= strain corresponding to yield strength of
nonprestressed steel reinforcement, in./in. (mm/mm)
= net tensile strain in extreme tension steel at
nominal strength, in./in. (mm/mm)
= transition strain in stress-strain curve of FRPconfined concrete, in./in. (mm/mm)
= strength reduction factor
= efficiency factor for FRP reinforcement in determination of fcc′ (based on geometry of cross
section)
= efficiency factor for FRP reinforcement in
determination of εccu (based on geometry of
cross section)
= bond-dependent coefficient for shear
= efficiency factor equal to 0.55 for FRP strain to
account for the difference between observed
rupture strain in confinement and rupture strain
determined from tensile tests
= FRP reinforcement ratio
= ratio of area of longitudinal steel reinforcement
to cross-sectional area of a compression member
(As /bh)
= ratio of nonprestressed reinforcement
= standard deviation
= average bond strength for NSM FRP bars, psi
(MPa)
= FRP strength reduction factor
= 0.85 for flexure (calibrated based on design
material properties)
= 0.85 for shear (based on reliability analysis) for
three-sided FRP U-wrap or two-sided strengthening schemes
= 0.95 for shear fully wrapped sections
2.2—Definitions and acronyms
The following definitions clarify terms pertaining to FRP
that are not commonly used in reinforced concrete practice.
These definitions are specific to this document, and are not
applicable to other ACI documents.
AFRP—aramid fiber-reinforced polymer.
440.2R-8
ACI COMMITTEE REPORT
batch—quantity of material mixed at one time or in one
continuous process.
binder—chemical treatment applied to the random
arrangement of fibers to give integrity to mats, roving, and
fabric. Specific binders are used to promote chemical
compatibility with the various laminating resins used.
carbon fiber-reinforced polymer (CFRP)—a composite
material comprising a polymer matrix reinforced with
carbon fiber cloth, mat, or strands.
catalyst—a substance that accelerates a chemical reaction
and enables it to proceed under conditions more mild than
otherwise required and that is not, itself, permanently
changed by the reaction. See initiator or hardener.
coating, intumescent—a covering that blisters to form a
heat shield when exposed to fire.
composite—engineering materials (for example, concrete
and fiber-reinforced polymer) made from two or more
constituent materials that remain distinct, but combine to
form materials with properties not possessed by any of the
constituent materials individually; the constituent materials
are generally characterized as matrix and reinforcement or
matrix and aggregate.
contact-critical application—strengthening or repair
system that relies on load transfer from the substrate to the
system material achieved through bearing or horizontal
shear transfer at the interface.
content, fiber—the amount of fiber present in a composite,
usually expressed as a percentage volume fraction or weight
fraction of the composite.
content, resin—the amount of resin in a fiber-reinforced
polymer composite laminate, expressed as either a percentage
of total mass or total volume.
creep-rupture—breakage of a material under sustained
loading at stresses less than the tensile strength.
cross-linking—forming covalent bonds linking one
polymer molecule to another (also polymerization). Note:
an increased number of cross-links per polymer molecule
increases strength and modulus at the expense of ductility.
cure, A-stage—early period after mixing at which
components of a thermosetting resin remain soluble and
fusible.
cure, B-stage—an intermediate period at which the
components of a thermosetting resin have reacted sufficiently
to produce a material that can be handled and processed, yet
not sufficiently to produce specified final properties.
cure, full—period at which components of a thermosetting
resin have reacted sufficiently for the resin to produce
specified final properties (antonym: undercure).
cure, thermosetting resin—inducing a reaction leading
to cross-linking in a thermosetting resin using chemical
initiators, catalysts, radiation, heat, or pressure.
curing agent—a catalytic or reactive agent that induces
cross-linking in a thermosetting resin (also hardener or
initiator).
debonding—failure of cohesive or adhesive bond at the
interface between a substrate and a strengthening or repair
system.
delamination—a planar separation in a material that is
roughly parallel to the surface of the material.
durability—the ability of a material to resist weathering
action, chemical attack, abrasion, and other conditions of
service.
e-glass—a family of glass with a calcium alumina borosilicate composition and a maximum alkali content of 2.0%. A
general-purpose fiber that is used in reinforced polymers.
epoxy—a thermosetting polymer that is the reaction
product of epoxy resin and an amino hardener (see also
resin, epoxy).
fabric—a two-dimensional network of woven, nonwoven,
knitted, or stitched fibers.
fiber—a slender and greatly elongated solid material,
generally with a length at least 100 times its diameter, that
has properties making it desirable for use as reinforcement.
fiber, aramid—fiber in which chains of aromatic polyamide
molecules are oriented along the fiber axis to exploit the
strength of the chemical bond.
fiber, carbon—fiber produced by heating organic
precursor materials containing a substantial amount of
carbon, such as rayon, polyacrylonitrile (PAN), or pitch in an
inert environment and at temperatures of 2700 °F (1500 °C)
or greater.
fiber, glass—filament drawn from an inorganic fusion
typically comprising silica-based material that has cooled
without crystallizing. Types of glass fibers include alkali
resistant (AR-glass), general purpose (E-glass), high
strength (S-glass), and boron free (ECR-glass).
fiber content—see content, fiber.
fiber fly—short filaments that break off dry fiber tows or
yarns during handling and become airborne; usually classified
as a nuisance dust.
fiber-reinforced polymer (FRP)—a general term for a
composite material comprising a polymer matrix reinforced
with fibers in the form of fabric, mat, strands, or any other
fiber form. See composite.
fiber volume fraction—the ratio of the volume of fibers
to the volume of the composite containing the fibers.
fiber weight fraction—the ratio of the weight of fibers to
the weight of the composite containing the fibers.
filament—see fiber.
filler—a finely divided, relatively inert material, such as
pulverized limestone, silica, or colloidal substances, added to
portland cement, paint, resin, or other materials to reduce
shrinkage, improve workability, reduce cost, or reduce density.
fire retardant—additive or coating used to reduce the
tendency of a resin to burn; these can be added to the resin or
coated on the surface of the FRP.
flow—movement of uncured resin under gravity loads or
differential pressure.
FRP—fiber-reinforced polymer.
glass fiber-reinforced polymer (GFRP)—a composite
material comprising a polymer matrix reinforced with glass
fiber cloth, mat, or strands.
grid, FRP—a rigid array of interconnected FRP elements
that can be used to reinforce concrete.
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
hardener—in a two-component adhesive or coating, the
chemical component that causes the resin component to cure.
impregnate—to saturate fibers with resin or binder.
initiator—a chemical (most commonly organic peroxides)
used to start the curing process for unsaturated polyester and
vinyl ester resins. See also catalyst.
lamina—a single layer of fabric or mat reinforcing bound
together in a cured resin matrix.
laminate—multiple plies or lamina molded together.
layup—the process of placing reinforcing material and
resin system in position for molding.
layup, wet—the process of placing the reinforcing material
in the mold or its final position and applying the resin as a
liquid.
length, development—the bonded length required to
achieve the design strength of a reinforcement at a critical
section.
load, sustained—a constant load that in structures is due
to dead load and long-term live load.
mat—a thin layer of randomly oriented chopped filaments,
short fibers (with or without a carrier fabric), or long random
filaments loosely held together with a binder and used as
reinforcement for a FRP composite material.
matrix—the resin or binders that hold the fibers in FRP
together, transfer load to the fibers, and protect them against
environmental attack and damage due to handling.
modulus of elasticity—the ratio of normal stress to
corresponding strain for tensile or compressive stress below
the proportional limit of the material; also referred to as
elastic modulus, Young’s modulus, and Young’s modulus of
elasticity; denoted by the symbol E.
monomer—an organic molecule of relatively low molecular
weight that creates a solid polymer by reacting with itself or
other compounds of low molecular weight.
NSM—near-surface-mounted.
pitch—viscid substance obtained as a residue of petroleum
or coal tar and used as a precursor in the manufacture of
some carbon fibers.
ply—see lamina.
polyacrylonitrile (PAN)—a polymer-based material that
is spun into a fiber form and used as a precursor in the
manufacturer of some carbon fibers.
polyester—one of a large group of synthetic resins,
mainly produced by reaction of dibasic acids with dihydroxy
alcohols; commonly prepared for application by mixing with
a vinyl-group monomer and free-radical catalysts at ambient
temperatures and used as binders for resin mortars and
concretes, fiber laminates (mainly glass), adhesives, and the
like. Commonly referred to as “unsaturated polyester.”
polymer—the product of polymerization; more commonly a
rubber or resin consisting of large molecules formed by
polymerization.
polymerization—the reaction in which two or more
molecules of the same substance combine to form a
compound containing the same elements and in the same
proportions but of higher molecular weight.
polyurethane—reaction product of an isocyanate with
any of a wide variety of other compounds containing an
440.2R-9
active hydrogen group; used to formulate tough, abrasionresistant coatings.
postcuring—application of elevated temperature to material
containing thermosetting resin to increase the level of polymer
cross-linking and enhance the final material properties. See
cure, thermosetting resin.
pot life—time interval, after mixing of thermosetting resin
and initiators, during which the mixture can be applied
without degrading the final performance of the resulting
polymer composite beyond specified limits.
prepreg—a sheet of fabric or mat containing resin or
binder usually advanced to the B-stage and ready for final
forming and cure.
pultrusion—a continuous process for manufacturing fiberreinforced polymer composites in which resin is impregnated
on fiber reinforcements (roving or mats) and are pulled
through a shaping and curing die, typically to produce
composites with uniform cross sections.
resin—generally a thermosetting polymer used as the
matrix and binder in FRP composites.
resin content—see content, resin.
resin, epoxy—a class of organic chemical bonding systems
used in the preparation of special coatings or adhesives for
concrete or as binders in epoxy-resin mortars, concretes, and
FRP composites.
resin, phenolic—a thermosetting resin produced by the
condensation reaction of an aromatic alcohol with an
aldehyde (usually a phenol with formaldehyde).
resin, thermoset—a material that hardens by an irreversible
three-dimensional cross-linking of monomers, typically
when subjected to heat or light energy and subsequently will
not soften.
roving—a parallel bundle of continuous yarns, tows, or
fibers with little or no twist.
shear, interlaminar—force tending to produce a relative
displacement along the plane of the interface between two
laminae.
shelf life—the length of time packaged materials can be
stored under specified conditions and remain usable.
sizing—surface treatment applied to filaments to impart
desired processing, durability, and bond attributes.
substrate—any material on the surface of which another
material is applied.
temperature, glass-transition—the midpoint of the
temperature range over which an amorphous material (such
as glass or a high polymer) changes from (or to) a brittle,
vitreous state to (or from) a plastic state.
thermoset—resin that is formed by cross-linking polymer
chains. Note: A thermoset cannot be melted and recycled
because the polymer chains form a three-dimensional network.
tow—an untwisted bundle of continuous filaments.
vinylester resin—a thermosetting reaction product of
epoxy resin with a polymerizable unsaturated acid (usually
methacrylic acid) that is then diluted with a reactive
monomer (usually styrene).
volatile organic compound (VOC)—an organic
compound that vaporizes under normal atmospheric conditions
and is defined by the U.S. Environmental Protection agency
440.2R-10
ACI COMMITTEE REPORT
CHAPTER 3—BACKGROUND INFORMATION
Externally bonded FRP systems have been used to
strengthen and retrofit existing concrete structures around the
world since the mid-1980s. The number of projects using FRP
systems worldwide has increased dramatically, from a few
20 years ago to several thousand today. Structural elements
strengthened with externally bonded FRP systems include
beams, slabs, columns, walls, joints/connections, chimneys
and smokestacks, vaults, domes, tunnels, silos, pipes, and
trusses. Externally bonded FRP systems have also been used
to strengthen masonry, timber, steel, and cast-iron structures.
The idea of strengthening concrete structures with externally
bonded reinforcement is not new. Externally bonded FRP
systems were developed as alternatives to traditional external
reinforcing techniques such as steel plate bonding and steel or
concrete column jacketing. The initial development of
externally bonded FRP systems for the retrofit of concrete
structures occurred in the 1980s in both Europe and Japan.
Researchers in the United States have had a long and
continuous interest in fiber-based reinforcement for concrete
structures since the 1930s. Development and research into
the use of these materials for retrofitting concrete structures,
however, started in the 1980s through the initiatives of the
National Science Foundation (NSF) and the Federal
Highway Administration (FHWA). The research activities
led to the construction of many field projects that encompassed a wide variety of environmental conditions. Previous
research and field applications for FRP rehabilitation and
strengthening are described in ACI 440R and conference
proceedings (Neale 2000; Dolan et al. 1999; Sheheta et al.
1999; Saadatmanesh and Ehsani 1998; Benmokrane and
Rahman 1998; Neale and Labossière 1997; Hassan and
Rizkalla 2002; Shield et al. 2005).
The development of codes and standards for externally
bonded FRP systems is ongoing in Europe, Japan, Canada,
and the United States. Within the last 10 years, the Japan
Society of Civil Engineers (JSCE), the Japan Concrete Institute
(JCI), and the Railway Technical Research Institute (RTRI)
published several documents related to the use of FRP
materials in concrete structures.
In Europe, Task Group 9.3 of the International Federation
for Structural Concrete (FIB) published a bulletin on design
guidelines for externally bonded FRP reinforcement for
reinforced concrete structures (International Federation for
Structural Concrete 2001).
The Canadian Standards Association (CSA) and ISIS have
been active in developing guidelines for FRP systems.
Section 16, “Fiber Reinforced Structures,” of the Canadian
Highway Bridge Design Code was completed in 2006
(CAN/CSA-S6-06), and CSA approved CSA S806-00.
In the United States, criteria for evaluating FRP systems
are available to the construction industry (ICBO AC125;
CALTRANS Division of Structures 1996; Hawkins et al. 1998).
3.1—Historical development
In Europe, FRP systems were developed as alternates to
steel plate bonding. Bonding steel plates to the tension zones
of concrete members with adhesive resins were shown to be
viable techniques for increasing their flexural strengths
(Fleming and King 1967). This technique has been used to
strengthen many bridges and buildings around the world.
Because steel plates can corrode, leading to a deterioration of
the bond between the steel and concrete, and because they
are difficult to install, requiring the use of heavy equipment,
researchers have looked to FRP materials as an alternative to
steel. Experimental work using FRP materials for retrofitting
concrete structures was reported as early as 1978 in Germany
(Wolf and Miessler 1989). Research in Switzerland led to the
first applications of externally bonded FRP systems to
reinforced concrete bridges for flexural strengthening
(Meier 1987; Rostasy 1987).
FRP systems were first applied to reinforced concrete
columns for providing additional confinement in Japan in the
1980s (Fardis and Khalili 1981; Katsumata et al. 1987). A
sudden increase in the use of FRPs in Japan was observed
after the 1995 Hyogoken-Nanbu earthquake (Nanni 1995).
3.2—Commercially available externally bonded
FRP systems
FRP systems come in a variety of forms, including wet
layup systems and precured systems. FRP system forms can
be categorized based on how they are delivered to the site
and installed. The FRP system and its form should be
selected based on the acceptable transfer of structural loads
and the ease and simplicity of application. Common FRP
system forms suitable for the strengthening of structural
members are listed in Sections 3.2.1 through 3.2.4.
3.2.1 Wet layup systems—Wet layup FRP systems consist
of dry unidirectional or multidirectional fiber sheets or
fabrics impregnated with a saturating resin on site. The
saturating resin, along with the compatible primer and putty,
bonds the FRP sheets to the concrete surface. Wet layup
systems are saturated in place and cured in place and, in this
sense, are analogous to cast-in-place concrete. Three common
types of wet layup systems are listed as follows:
1. Dry unidirectional fiber sheets where the fibers run
predominantly in one planar direction;
2. Dry multidirectional fiber sheets or fabrics where the
fibers are oriented in at least two planar directions; and
as any compound of carbon, excluding carbon monoxide,
carbon dioxide, carbonic acid, metallic carbides or carbonates,
and ammonium carbonate, which participates in atmospheric
photochemical reactions.
volume fraction—see fiber volume fraction.
wet layup—see layup, wet.
wet-out—the process of coating or impregnating roving,
yarn, or fabric to fill the voids between the strands and
filaments with resin; it is also the condition at which this
state is achieved.
witness panel—a small mockup manufactured under
conditions representative of field application, to confirm that
prescribed procedures and materials will yield specified
mechanical and physical properties.
yarn—a twisted bundle of continuous filaments.
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
3. Dry fiber tows that are wound or otherwise mechanically
applied to the concrete surface. The dry fiber tows are
impregnated with resin on site during the winding operation.
3.2.2 Prepreg systems—Prepreg FRP systems consist of
partially cured unidirectional or multidirectional fiber sheets
or fabrics that are preimpregnated with a saturating resin in
the manufacturer’s facility. Prepreg systems are bonded to
the concrete surface with or without an additional resin
application, depending on specific system requirements.
Prepreg systems are saturated off-site and, like wet layup
systems, cured in place. Prepreg systems usually require
additional heating for curing. Prepreg system manufacturers
should be consulted for storage and shelf-life recommendations
and curing procedures. Three common types of prepreg FRP
systems are:
1. Preimpregnated unidirectional fiber sheets where the
fibers run predominantly in one planar direction;
2. Preimpregnated multidirectional fiber sheets or fabrics
where the fibers are oriented in at least two planar directions;
and
3. Preimpregnated fiber tows that are wound or otherwise
mechanically applied to the concrete surface.
3.2.3 Precured systems—Precured FRP systems consist of a
wide variety of composite shapes manufactured off site.
Typically, an adhesive, along with the primer and putty, is
used to bond the precured shapes to the concrete surface. The
system manufacturer should be consulted for recommended
installation procedures. Precured systems are analogous to
precast concrete. Three common types of precured systems are:
1. Precured unidirectional laminate sheets, typically
delivered to the site in the form of large flat stock or as thin
ribbon strips coiled on a roll;
2. Precured multidirectional grids, typically delivered to
the site coiled on a roll; and
3. Precured shells, typically delivered to the site in the
form of shell segments cut longitudinally so they can be
opened and fitted around columns or other members;
multiple shell layers are bonded to the concrete and to each
other to provide seismic confinement.
3.2.4 Near-surface-mounted (NSM) systems—Surfaceembedded (NSM) FRP systems consist of circular or rectangular bars or plates installed and bonded into grooves made
on the concrete surface. A suitable adhesive is used to bond
the FRP bar into the groove, and is cured in-place. The NSM
system manufacturer should be consulted for recommended
adhesives. Two common FRP bar types used for NSM
applications are:
1. Round bars usually manufactured using pultrusion
processes, typically delivered to the site in the form of single
bars or in a roll depending on bar diameter; and
2. Rectangular bars and plates usually manufactured using
pultrusion processes, typically delivered to the site in a roll.
PART 2—MATERIALS
CHAPTER 4—CONSTITUENT
MATERIALS AND PROPERTIES
The physical and mechanical properties of FRP materials
presented in this chapter explain the behavior and properties
440.2R-11
affecting their use in concrete structures. The effects of
factors such as loading history and duration, temperature,
and moisture on the properties of FRP are discussed.
FRP strengthening systems come in a variety of forms
(wet layup, prepreg, and precured). Factors such as fiber
volume, type of fiber, type of resin, fiber orientation,
dimensional effects, and quality control during manufacturing
all play a role in establishing the characteristics of an FRP
material. The material characteristics described in this
chapter are generic and do not apply to all commercially
available products. Standard test methods are being developed
by several organizations, including ASTM, ACI, and CSA,
to characterize certain FRP products. In the interim, however,
the licensed design professional is encouraged to consult
with the FRP system manufacturer to obtain the relevant
characteristics for a specific product and the applicability of
those characteristics.
4.1—Constituent materials
The constituent materials used in commercially available
FRP repair systems, including all resins, primers, putties,
saturants, adhesives, and fibers, have been developed for the
strengthening of structural concrete members based on
materials and structural testing.
4.1.1 Resins—A wide range of polymeric resins, including
primers, putty fillers, saturants, and adhesives, are used with
FRP systems. Commonly used resin types, including epoxy,
vinyl esters, and polyesters, have been formulated for use in
a wide range of environmental conditions. FRP system
manufacturers use resins that have:
• Compatibility with and adhesion to the concrete
substrate;
• Compatibility with and adhesion to the FRP composite
system;
• Resistance to environmental effects, including but not
limited to moisture, salt water, temperature extremes, and
chemicals normally associated with exposed concrete;
• Filling ability;
• Workability;
• Pot life consistent with the application; and
• Compatibility with and adhesion to the reinforcing
fiber; and
• Development of appropriate mechanical properties for
the FRP composite.
4.1.1.1 Primer—Primer is used to penetrate the surface
of the concrete, providing an improved adhesive bond for the
saturating resin or adhesive.
4.1.1.2 Putty fillers—Putty is used to fill small surface
voids in the substrate, such as bug holes, and to provide a
smooth surface to which the FRP system can bond. Filled
surface voids also prevent bubbles from forming during
curing of the saturating resin.
4.1.1.3 Saturating resin—Saturating resin is used to
impregnate the reinforcing fibers, fix them in place, and
provide a shear load path to effectively transfer load between
fibers. The saturating resin also serves as the adhesive for
wet layup systems, providing a shear load path between the
previously primed concrete substrate and the FRP system
440.2R-12
ACI COMMITTEE REPORT
Table 4.1—Typical densities of FRP materials,
lb/ft3 (g/cm3)
•
Steel
GFRP
CFRP
AFRP
490 (7.9) 75 to 130 (1.2 to 2.1) 90 to 100 (1.5 to 1.6) 75 to 90 (1.2 to 1.5)
Table 4.2—Typical coefficients of thermal
expansion for FRP materials*
•
Coefficient of thermal expansion, × 10–6/°F (× 10–6/°C)
Direction
Longitudinal, αL
Longitudinal, αT
GFRP
3.3 to 5.6
(6 to 10)
10.4 to 12.6
(19 to 23)
CFRP
–0.6 to 0
(–1 to 0)
12 to 27
(22 to 50)
AFRP
–3.3 to –1.1
(–6 to –2)
33 to 44
(60 to 80)
•
*Typical values for fiber-volume fractions ranging from 0.5 to 0.7.
4.1.1.4 Adhesives—Adhesives are used to bond precured
FRP laminate and NSM systems to the concrete substrate. The
adhesive provides a shear load path between the concrete
substrate and the FRP reinforcing system. Adhesives are also
used to bond together multiple layers of precured FRP laminates.
4.1.2 Fibers—Continuous glass, aramid, and carbon fibers
are common reinforcements used with FRP systems. The
fibers give the FRP system its strength and stiffness. Typical
ranges of the tensile properties of fibers are given in
Appendix A. A more detailed description of fibers is given
in ACI 440R.
4.1.3 Protective coatings—The protective coating protects
the bonded FRP reinforcement from potentially damaging
environmental and mechanical effects. Coatings are typically
applied to the exterior surface of the cured FRP system after
the adhesive or saturating resin has cured. The protection
systems are available in a variety of forms. These include:
• Polymer coatings that are generally epoxy or polyurethanes;
• Acrylic coatings that can be either straight acrylic
systems or acrylic cement-based systems. The acrylic
systems can also come in different textures;
• Cementitious systems that may require roughening of
the FRP surface (such as broadcasting sand into wet
resin) and can be installed in the same manner as they
would be installed on a concrete surface; and
• Intumescent coatings that are polymer-based coatings
used to control flame spread and smoke generation per
code requirements.
There are several reasons why protection systems are used
to protect FRP systems that have been installed on concrete
surfaces. These include:
• Ultraviolet light protection—The epoxy used as part of
the FRP strengthening system will be affected over
time by exposure to ultraviolet light. There are a
number of available methods used to protect the system
from ultraviolet light. These include: acrylic coatings,
cementitious surfacing, aliphatic polyurethane coatings,
and others. Certain types of vinylester resins have
higher ultraviolet light durability than epoxy resins;
• Fire protection—Fire protection systems are discussed
in Sections 1.3.2 and 9.2.1;
•
•
Vandalism—Protective systems that are to resist
vandalism should be hard and durable. There are different
levels of vandalism protection from polyurethane coatings
that will resist cutting and scraping to cementitious
overlays that provide much more protection;
Impact, abrasion, and wear—Protection systems for
impact, abrasion, and wear are similar to those used for
vandalism protection; however, abrasion and wear are
different than vandalism in that they result from
continuous exposure rather than a one-time event, and
their protection systems are usually chosen for their
hardness and durability;
Aesthetics—Protective topcoats may be used to conceal
the FRP system. These may be acrylic latex coatings
that are gray in color to match bare concrete, or they
may be various other colors and textures to match the
existing structure;
Chemical resistance—Exposure to harsh chemicals,
such as strong acids, may damage the FRP system. In
such environments, coatings with better chemical
resistance, such as urethanes and novolac epoxies, may
be used; and
Submersion in potable water—In applications where
the FRP system is to be submerged in potable water, the
FRP system may leach compounds into the water
supply. Protective coatings that do not leach harmful
chemicals into the water may be used as a barrier
between the FRP system and the potable water supply.
4.2—Physical properties
4.2.1 Density—FRP materials have densities ranging from
75 to 130 lb/ft3 (1.2 to 2.1 g/cm3), which is four to six times
lower than that of steel (Table 4.1). The reduced density
leads to lower transportation costs, reduces added dead load
on the structure, and can ease handling of the materials on
the project site.
4.2.2 Coefficient of thermal expansion—The coefficients
of thermal expansion of unidirectional FRP materials differ
in the longitudinal and transverse directions, depending on
the types of fiber, resin, and volume fraction of fiber. Table 4.2
lists the longitudinal and transverse coefficients of thermal
expansion for typical unidirectional FRP materials. Note that
a negative coefficient of thermal expansion indicates that the
material contracts with increased temperature and expands
with decreased temperature. For reference, concrete has a
coefficient of thermal expansion that varies from 4 × 10–6 to
6 × 10–6/°F (7 × 10–6 to 11 × 10–6/°C), and is usually assumed
to be isotropic (Mindess and Young 1981). Steel has an
isotropic coefficient of thermal expansion of 6.5 × 10–6/°F
(11.7 × 10–6/°C). See Section 9.3.1 for design considerations
regarding thermal expansion.
4.2.3 Effects of high temperatures—Beyond the Tg, the
elastic modulus of a polymer is significantly reduced due to
changes in its molecular structure. The value of Tg depends
on the type of resin but is normally in the region of 140 to
180 °F (60 to 82 °C). In an FRP composite material, the
fibers, which exhibit better thermal properties than the resin,
can continue to support some load in the longitudinal direction
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
until the temperature threshold of the fibers is reached. This
can occur at temperatures exceeding 1800 °F (1000 °C) for
carbon fibers, and 350 °F (175 °C) for aramid fibers. Glass
fibers are capable of resisting temperatures in excess of 530 °F
(275 °C). Due to a reduction in force transfer between fibers
through bond to the resin, however, the tensile properties of the
overall composite are reduced. Test results have indicated
that temperatures of 480 °F (250 °C), much higher than the
resin Tg, will reduce the tensile strength of GFRP and CFRP
materials in excess of 20% (Kumahara et al. 1993). Other
properties affected by the shear transfer through the resin,
such as bending strength, are reduced significantly at lower
temperatures (Wang and Evans 1995).
For bond-critical applications of FRP systems, the properties
of the polymer at the fiber-concrete interface are essential in
maintaining the bond between FRP and concrete. At a
temperature close to its Tg, however, the mechanical properties
of the polymer are significantly reduced, and the polymer
begins to lose its ability to transfer stresses from the concrete
to the fibers.
4.3—Mechanical properties
4.3.1 Tensile behavior—When loaded in direct tension,
unidirectional FRP materials do not exhibit any plastic
behavior (yielding) before rupture. The tensile behavior of
FRP materials consisting of one type of fiber material is
characterized by a linear elastic stress-strain relationship
until failure, which is sudden and brittle.
The tensile strength and stiffness of an FRP material is
dependent on several factors. Because the fibers in an FRP
material are the main load-carrying constituents, the type of
fiber, the orientation of fibers, the quantity of fibers, and
method and conditions in which the composite is produced
affect the tensile properties of the FRP material. Due to the
primary role of the fibers and methods of application, the
properties of an FRP repair system are sometimes reported
based on the net-fiber area. In other instances, such as in
precured laminates, the reported properties are based on the
gross-laminate area.
The gross-laminate area of an FRP system is calculated
using the total cross-sectional area of the cured FRP system,
including all fibers and resin. The gross-laminate area is
typically used for reporting precured laminate properties
where the cured thickness is constant and the relative proportion
of fiber and resin is controlled.
The net-fiber area of an FRP system is calculated using the
known area of fiber, neglecting the total width and thickness
of the cured system; thus, resin is excluded. The net-fiber
area is typically used for reporting properties of wet layup
systems that use manufactured fiber sheets and fieldinstalled resins. The wet layup installation process leads to
controlled fiber content and variable resin content.
System properties reported using the gross-laminate area
have higher relative thickness dimensions and lower relative
strength and modulus values, whereas system properties
reported using the net-fiber area have lower relative thickness
dimensions and higher relative strength and modulus values.
Regardless of the basis for the reported values, the load-
440.2R-13
carrying strength (ffu Af ) and axial stiffness (Af Ef) of the
composite remain constant. (The calculation of FRP system
properties using both gross-laminate and net-fiber property
methods is illustrated in Part 5.) Properties reported based on
the net-fiber area are not the properties of the bare fibers.
When tested as a part of a cured composite, the measured
tensile strength and ultimate rupture strain of the net-fiber
are typically lower than those measured based on a dry fiber
test. The properties of an FRP system should be characterized
as a composite, recognizing not just the material properties
of the individual fibers, but also the efficiency of the fiberresin system, the fabric architecture, and the method used to
create the composite. The mechanical properties of all FRP
systems, regardless of form, should be based on the testing
of laminate samples with known fiber content.
The tensile properties of some commercially available
FRP strengthening systems are given in Appendix A. The
tensile properties of a particular FRP system, however, can
be obtained from the FRP system manufacturer or using the
test appropriate method as described in ACI 440.3R and
ASTM D3039 and D7205. Manufacturers should report an
ultimate tensile strength, which is defined as the mean tensile
strength of a sample of test specimens minus three times the
standard deviation (ffu* = f fu – 3σ) and, similarly, report an
* = ε – 3σ). This approach provides
ultimate rupture strain (εfu
fu
a 99.87% probability that the actual ultimate tensile properties
will exceed these statistically-based design values for a standard
sample distribution (Mutsuyoshi et al. 1990). Young’s
modulus should be calculated as the chord modulus between
0.003 and 0.006 strain, in accordance with ASTM D3039. A
minimum number of 20 replicate test specimens should be
used to determine the ultimate tensile properties. The
manufacturer should provide a description of the method
used to obtain the reported tensile properties, including the
number of tests, mean values, and standard deviations.
4.3.2 Compressive behavior—Externally bonded FRP
systems should not be used as compression reinforcement
due to insufficient testing validating its use in this type of
application. While it is not recommended to rely on externally
bonded FRP systems to resist compressive stresses, the
following section is presented to fully characterize the
behavior of FRP materials.
Coupon tests on FRP laminates used for repair on concrete
have shown that the compressive strength of FRP is lower
than the tensile strength (Wu 1990). The mode of failure for
FRP laminates subjected to longitudinal compression can
include transverse tensile failure, fiber microbuckling, or
shear failure. The mode of failure depends on the type of
fiber, the fiber-volume fraction, and the type of resin.
Compressive strengths of 55, 78, and 20% of the tensile
strength have been reported for GFRP, CFRP, and AFRP,
respectively (Wu 1990). In general, compressive strengths
are higher for materials with higher tensile strengths, except
in the case of AFRP, where the fibers exhibit nonlinear
behavior in compression at a relatively low level of stress.
The compressive modulus of elasticity is usually smaller
than the tensile modulus of elasticity of FRP materials. Test
reports on samples containing a 55 to 60% volume fraction
440.2R-14
ACI COMMITTEE REPORT
of continuous E-glass fibers in a matrix of vinyl ester or
isophthalic polyester resin have indicated a compressive
modulus of elasticity of 5000 to 7000 ksi (34,000 to 48,000
MPa) (Wu 1990). According to reports, the compressive
modulus of elasticity is approximately 80% for GFRP, 85%
for CFRP, and 100% for AFRP of the tensile modulus of
elasticity for the same product (Ehsani 1993).
4.4—Time-dependent behavior
4.4.1 Creep-rupture—FRP materials subjected to a
constant load over time can suddenly fail after a time period
referred to as the endurance time. This type of failure is
known as creep-rupture. As the ratio of the sustained tensile
stress to the short-term strength of the FRP laminate increases,
endurance time decreases. The endurance time also decreases
under adverse environmental conditions, such as high
temperature, ultraviolet-radiation exposure, high alkalinity,
wet and dry cycles, or freezing-and-thawing cycles.
In general, carbon fibers are the least susceptible to creeprupture; aramid fibers are moderately susceptible, and glass
fibers are most susceptible. Creep-rupture tests have been
conducted on 0.25 in. (6 mm) diameter FRP bars reinforced
with glass, aramid, and carbon fibers. The FRP bars were
tested at different load levels at room temperature. Results
indicated that a linear relationship exists between creeprupture strength and the logarithm of time for all load levels.
The ratios of stress level at creep-rupture after 500,000 hours
(about 50 years) to the initial ultimate strength of the GFRP,
AFRP, and CFRP bars were extrapolated to be approximately
0.3, 0.5, and 0.9, respectively (Yamaguchi et al. 1997;
Malvar 1998). Recommendations on sustained stress limits
imposed to avoid creep-rupture are given in the design
section of this guide. As long as the sustained stress in the
FRP is below the creep rupture stress limits, the strength of
the FRP is available for nonsustained loads.
4.4.2 Fatigue—A substantial amount of data for fatigue
behavior and life prediction of stand-alone FRP materials is
available (National Research Council 1991). Most of these
data were generated from materials typically used by the
aerospace industry. Despite the differences in quality and
consistency between aerospace and commercial-grade FRP
materials, some general observations on the fatigue behavior
of FRP materials can be made. Unless specifically stated
otherwise, the following cases being reviewed are based on
a unidirectional material with approximately 60% fibervolume fraction and subjected to tension-tension sinusoidal
cyclic loading at:
• A frequency low enough to not cause self-heating;
• Ambient laboratory environments;
• A stress ratio (ratio of minimum applied stress to
maximum applied stress) of 0.1; and
• A direction parallel to the principal fiber alignment.
Test conditions that raise the temperature and moisture
content of FRP materials generally degrade the ambient
environment fatigue behavior.
Of all types of FRP composites for infrastructure applications,
CFRP is the least prone to fatigue failure. An endurance limit
of 60 to 70% of the initial static ultimate strength of CFRP is
typical. On a plot of stress versus the logarithm of the
number of cycles at failure (S-N curve), the downward slope
for CFRP is usually approximately 5% of the initial static
ultimate strength per decade of logarithmic life. At 1 million
cycles, the fatigue strength is generally between 60 and 70%
of the initial static ultimate strength and is relatively unaffected
by the moisture and temperature exposures of concrete
structures unless the resin or fiber/resin interface is substantially
degraded by the environment.
In ambient-environment laboratory tests (Mandell and
Meier 1983), individual glass fibers demonstrated delayed
rupture caused by stress corrosion, which had been induced
by the growth of surface flaws in the presence of even minute
quantities of moisture. When many glass fibers were
embedded into a matrix to form an FRP composite, a cyclic
tensile fatigue effect of approximately 10% loss in the initial
static strength per decade of logarithmic lifetime was
observed (Mandell 1982). This fatigue effect is thought to be
due to fiber-fiber interactions and is not dependent on the
stress corrosion mechanism described for individual fibers.
Usually, no clear fatigue limit can be defined. Environmental
factors can play an important role in the fatigue behavior of
glass fibers due to their susceptibility to moisture, alkaline,
or acidic solutions.
Aramid fibers, for which substantial durability data are
available, appear to behave reasonably well in fatigue.
Neglecting in this context the rather poor durability of all
aramid fibers in compression, the tension-tension fatigue
behavior of an impregnated aramid fiber strand is excellent.
Strength degradation per decade of logarithmic lifetime is
approximately 5 to 6% (Roylance and Roylance 1981). While
no distinct endurance limit is known for AFRP, 2-million-cycle
endurance limits of commercial AFRP tendons for concrete
applications have been reported in the range of 54 to 73% of
the ultimate tensile strength (Odagiri et al. 1997). Based on
these findings, Odagiri et al. suggested that the maximum
stress be set to 0.54 to 0.73 times the tensile strength.
Because the slope of the applied stress versus logarithmic
endurance time of AFRP is similar to the slope of the stress
versus logarithmic cyclic lifetime data, the individual fibers
appear to fail by a strain-limited, creep-rupture process. This
lifetime-limiting mechanism in commercial AFRP bars is
accelerated by exposure to moisture and elevated temperature
(Roylance and Roylance 1981; Rostasy 1997).
4.5—Durability
Many FRP systems exhibit reduced mechanical properties
after exposure to certain environmental factors, including
high temperature, humidity, and chemical exposure. The
exposure environment, duration of the exposure, resin type
and formulation, fiber type, and resin-curing method are
some of the factors that influence the extent of the reduction
in mechanical properties. These factors are discussed in
more detail in Section 9.3. The tensile properties reported by
the manufacturer are based on testing conducted in a laboratory
environment, and do not reflect the effects of environmental
exposure. These properties should be adjusted in accordance
with Section 9.4 to account for the anticipated service
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
environment to which the FRP system may be exposed
during its service life.
4.6—FRP systems qualification
FRP systems should be qualified for use on a project on
the basis of independent laboratory test data of the FRPconstituent materials and the laminates made with them,
structural test data for the type of application being considered,
and durability data representative of the anticipated environment. Test data provided by the FRP system manufacturer
demonstrating the proposed FRP system should meet all
mechanical and physical design requirements, including
tensile strength, durability, resistance to creep, bond to
substrate, and Tg, should be considered.
FRP composite systems that have not been fully tested
should not be considered for use. Mechanical properties of
FRP systems should be determined from tests on laminates
manufactured in a process representative of their field
installation. Mechanical properties should be tested in
general conformance with the procedures listed in Appendix B.
Modifications of standard testing procedures may be
permitted to emulate field assemblies.
The specified material-qualification programs should
require sufficient laboratory testing to measure the repeatability and reliability of critical properties. Testing of multiple
batches of FRP materials is recommended. Independent
structural testing can be used to evaluate a system’s
performance for the specific application.
PART 3—RECOMMENDED
CONSTRUCTION REQUIREMENTS
CHAPTER 5—SHIPPING,
STORAGE, AND HANDLING
5.1—Shipping
FRP system constituent materials should be packaged and
shipped in a manner that conforms to all applicable federal
and state packaging and shipping codes and regulations.
Packaging, labeling, and shipping for thermosetting resin
materials are controlled by CFR 49. Many materials are
classified as corrosive, flammable, or poisonous in Subchapter C
(CFR 49) under “Hazardous Materials Regulations.”
5.2—Storage
5.2.1 Storage conditions—To preserve the properties and
maintain safety in the storage of FRP system constituent
materials, the materials should be stored in accordance with
the manufacturer’s recommendations. Certain constituent
materials, such as reactive curing agents, hardeners, initiators,
catalysts, and cleaning solvents, have safety-related requirements, and should be stored in a manner as recommended by
the manufacturer and OSHA. Catalysts and initiators
(usually peroxides) should be stored separately.
5.2.2 Shelf life—The properties of the uncured resin
components can change with time, temperature, or humidity.
Such conditions can affect the reactivity of the mixed system
and the uncured and cured properties. The manufacturer sets
a recommended shelf life within which the properties of the
resin-based materials should continue to meet or exceed
440.2R-15
stated performance criteria. Any component material that
has exceeded its shelf life, has deteriorated, or has been
contaminated should not be used. FRP materials deemed
unusable should be disposed of in a manner specified by the
manufacturer and acceptable to state and federal environmental
control regulations.
5.3—Handling
5.3.1 Material safety data sheet—Material safety data
sheets (MSDS) for all FRP constituent materials and
components should be obtained from the manufacturers, and
should be accessible at the job site.
5.3.2 Information sources—Detailed information on the
handling and potential hazards of FRP constituent materials
can be found in information sources, such as ACI and ICRI
reports, company literature and guides, OSHA guidelines,
and other government informational documents. ACI 503R
is specifically noted as a general guideline for the safe
handling of epoxy and other resin adhesive compounds.
5.3.3 General handling hazards—Thermosetting resins
describe a generic family of products that includes unsaturated
polyesters, vinyl esters, epoxy, and polyurethane resins. The
materials used with them are generally described as hardeners,
curing agents, peroxide initiators, isocyanates, fillers, and
flexibilizers. There are precautions that should be observed
when handling thermosetting resins and their component
materials. Some general hazards that may be encountered
when handling thermosetting resins are listed as:
• Skin irritation, such as burns, rashes, and itching;
• Skin sensitization, which is an allergic reaction similar
to that caused by poison ivy, building insulation, or
other allergens;
• Breathing organic vapors from cleaning solvents,
monomers, and dilutents;
• With a sufficient concentration in air, explosion or fire
of flammable materials when exposed to heat, flames,
pilot lights, sparks, static electricity, cigarettes, or other
sources of ignition;
• Exothermic reactions of mixtures of materials causing
fires or personal injury; and
• Nuisance dust caused by grinding or handling of the
cured FRP materials (manufacturer’s literature should
be consulted for specific hazards).
The complexity of thermosetting resins and associated
materials makes it essential that labels and the MSDS are
read and understood by those working with these products.
CFR 16, Part 1500, regulates the labeling of hazardous
substances and includes thermosetting-resin materials. ANSI
Z-129.1 provides further guidance regarding classification and
precautions.
5.3.4 Personnel safe handling and clothing—Disposable
suits and gloves are suitable for handling fiber and resin
materials. Disposable rubber or plastic gloves are recommended and should be discarded after each use. Gloves
should be resistant to resins and solvents. Safety glasses or
goggles should be used when handling resin components and
solvents. Respiratory protection, such as dust masks or
respirators, should be used when fiber fly, dust, or organic
440.2R-16
ACI COMMITTEE REPORT
vapors are present, or during mixing and placing of resins if
required by the FRP system manufacturer.
5.3.5 Workplace safe handling—The workplace should be
well ventilated. Surfaces should be covered as needed to
protect against contamination and resin spills. Each FRP
system constituent material has different handling and
storage requirements to prevent damage. The material
manufacturer should be consulted for guidance. Some resin
systems are potentially dangerous during mixing of the
components. The manufacturer’s literature should be
consulted for proper mixing procedures, and the MSDS for
specific handling hazards. Ambient cure resin formulations
produce heat when curing, which in turn accelerates the
reaction. Uncontrolled reactions, including fuming, fire, or
violent boiling, may occur in containers holding a mixed
mass of resin; therefore, containers should be monitored.
5.3.6 Cleanup and disposal—Cleanup can involve use of
flammable solvents, and appropriate precautions should be
observed. Cleanup solvents are available that do not present
the same flammability concerns. All waste materials should
be contained and disposed of as prescribed by the prevailing
environmental authority.
CHAPTER 6—INSTALLATION
Procedures for installing FRP systems have been developed
by the system manufacturers and often differ between
systems. In addition, installation procedures can vary within
a system, depending on the type and condition of the structure.
This chapter presents general guidelines for the installation
of FRP systems. Contractors trained in accordance with the
installation procedures developed by the system manufacturer
should install FRP systems. Deviations from the procedures
developed by the FRP system manufacturer should not be
allowed without consulting with the manufacturer.
6.1—Contractor competency
The FRP system installation contractor should demonstrate
competency for surface preparation and application of the
FRP system to be installed. Contractor competency can be
demonstrated by providing evidence of training and
documentation of related work previously completed by the
contractor or by actual surface preparation and installation of
the FRP system on portions of the structure. The FRP system
manufacturer or its authorized agent should train the
contractor’s application personnel in the installation procedures
of its system and ensure they are competent to install the
system.
6.2—Temperature, humidity, and moisture
considerations
Temperature, relative humidity, and surface moisture at
the time of installation can affect the performance of the FRP
system. Conditions to be observed before and during
installation include surface temperature of the concrete, air
temperature, relative humidity, and corresponding dew point.
Primers, saturating resins, and adhesives should generally
not be applied to cold or frozen surfaces. When the surface
temperature of the concrete surface falls below a minimum
level as specified by the FRP system manufacturer, improper
saturation of the fibers and improper curing of the resin
constituent materials can occur, compromising the integrity
of the FRP system. An auxiliary heat source can be used to
raise the ambient and surface temperature during installation.
The heat source should be clean and not contaminate the
surface or the uncured FRP system.
Resins and adhesives should generally not be applied to
damp or wet surfaces unless they have been formulated for
such applications. FRP systems should not be applied to
concrete surfaces that are subject to moisture vapor transmission. The transmission of moisture vapor from a concrete
surface through the uncured resin materials typically appears
as surface bubbles and can compromise the bond between
the FRP system and the substrate.
6.3—Equipment
Some FRP systems have unique equipment designed
specifically for the application of the materials for one particular
system. This equipment can include resin impregnators,
sprayers, lifting/positioning devices, and winding machines.
All equipment should be clean and in good operating condition.
The contractor should have personnel trained in the operation
of all equipment. Personal protective equipment, such as
gloves, masks, eye guards, and coveralls, should be chosen
and worn for each employee’s function. All supplies and
equipment should be available in sufficient quantities to allow
continuity in the installation project and quality assurance.
6.4—Substrate repair and surface preparation
The behavior of concrete members strengthened or retrofitted with FRP systems is highly dependent on a sound
concrete substrate and proper preparation and profiling of
the concrete surface. An improperly prepared surface can
result in debonding or delamination of the FRP system before
achieving the design load transfer. The general guidelines
presented in this chapter should be applicable to all externally
bonded FRP systems. Specific guidelines for a particular
FRP system should be obtained from the FRP system
manufacturer. Substrate preparation can generate noise,
dust, and disruption to building occupants.
6.4.1 Substrate repair—All problems associated with the
condition of the original concrete and the concrete substrate
that can compromise the integrity of the FRP system should
be addressed before surface preparation begins. ACI 546R
and ICRI 03730 detail methods for the repair and surface
preparation of concrete. All concrete repairs should meet the
requirements of the design drawings and project specifications.
The FRP system manufacturer should be consulted on the
compatibility of the FRP system with materials used for
repairing the substrate.
6.4.1.1 Corrosion-related deterioration—Externally
bonded FRP systems should not be applied to concrete
substrates suspected of containing corroded reinforcing
steel. The expansive forces associated with the corrosion
process are difficult to determine, and could compromise the
structural integrity of the externally applied FRP system.
The cause(s) of the corrosion should be addressed, and the
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
corrosion-related deterioration should be repaired before the
application of any externally bonded FRP system.
6.4.1.2 Injection of cracks—Cracks that are 0.010 in.
(0.3 mm) and wider can affect the performance of the externally
bonded FRP system through delamination or fiber crushing.
Consequently, cracks wider than 0.010 in. (0.3 mm) should
be pressure injected with epoxy before FRP installation in
accordance with ACI 224.1R. Smaller cracks exposed to
aggressive environments may require resin injection or
sealing to prevent corrosion of existing steel reinforcement.
Crack-width criteria for various exposure conditions are
given in ACI 224.1R.
6.4.2 Surface preparation—Surface preparation requirements
should be based on the intended application of the FRP
system. Applications can be categorized as bond-critical or
contact-critical. Bond-critical applications, such as flexural
or shear strengthening of beams, slabs, columns, or walls,
require an adhesive bond between the FRP system and the
concrete. Contact-critical applications, such as confinement
of columns, only require intimate contact between the FRP
system and the concrete. Contact-critical applications do not
require an adhesive bond between the FRP system and the
concrete substrate, although one is often provided to facilitate
installation.
6.4.2.1 Bond-critical applications—Surface preparation
for bond-critical applications should be in accordance with
recommendations of ACI 546R and ICRI 03730. The
concrete or repaired surfaces to which the FRP system is to
be applied should be freshly exposed and free of loose or
unsound materials. Where fibers wrap around the corners of
rectangular cross sections, the corners should be rounded to
a minimum 0.5 in. (13 mm) radius to prevent stress
concentrations in the FRP system and voids between the
FRP system and the concrete. Roughened corners should be
smoothed with putty. Obstructions, inside corners, concave
surfaces, and embedded objects can affect the performance
of the FRP system, and should be addressed. Obstructions
and embedded objects may need to be removed before
installing the FRP system. Inside corners and concave surfaces
may require special detailing to ensure that the bond of the
FRP system to the substrate is maintained. Surface preparation
can be accomplished using abrasive or water-blasting
techniques. All laitance, dust, dirt, oil, curing compound,
existing coatings, and any other matter that could interfere
with the bond of the FRP system to the concrete should be
removed. Bug holes and other small surface voids should be
completely exposed during surface profiling. After the profiling
operations are complete, the surface should be cleaned and
protected before FRP installation so that no materials that
can interfere with bond are redeposited on the surface.
The concrete surface should be prepared to a minimum
concrete surface profile (CSP) 3 as defined by the ICRIsurface-profile chips. The FRP system manufacturer should
be consulted to determine if more aggressive surface
profiling is necessary. Localized out-of-plane variations,
including form lines, should not exceed 1/32 in. (1 mm) or
the tolerances recommended by the FRP system manufacturer.
Localized out-of-plane variations can be removed by
440.2R-17
grinding, before abrasive or water blasting, or can be
smoothed over using resin-based putty if the variations are
very small. Bug holes and voids should be filled with resinbased putty.
All surfaces to receive the strengthening system should be
as dry as recommended by the FRP system manufacturer.
Water in the pores can inhibit resin penetration and reduce
mechanical interlock. Moisture content should be evaluated
in accordance with the requirements of ACI 503.4.
6.4.2.2 Contact-critical applications—In applications
involving confinement of structural concrete members,
surface preparation should promote continuous intimate
contact between the concrete surface and the FRP system.
Surfaces to be wrapped should, at a minimum, be flat or
convex to promote proper loading of the FRP system. Large
voids in the surface should be patched with a repair material
compatible with the existing concrete.
Materials with low compressive strength and elastic
modulus, such as plaster, can reduce the effectiveness of the
FRP system and should be removed.
6.4.3 Surface-embedded systems—NSM systems are
typically installed in grooves cut onto the concrete surface.
The existing steel reinforcement should not be damaged
while cutting the groove. The soundness of the concrete
surface should be checked before installing the bar. The
inside faces of the groove should be cleaned to ensure
adequate bond with concrete. The resulting groove should be
free of laitance or other compounds that may interfere with
bond. The moisture content of the parent concrete should be
controlled to suit the bonding properties of the adhesive. The
grooves should be completely filled with the adhesive. The
adhesive should be specified by the NSM system manufacturer.
6.5—Mixing of resins
Mixing of resins should be done in accordance with the
FRP system manufacturer’s recommended procedure. All
resin components should be at the proper temperature and
mixed in the correct ratio until there is a uniform and
complete mixing of components. Resin components are often
contrasting colors, so full mixing is achieved when color
streaks are eliminated. Resins should be mixed for the
prescribed mixing time and visually inspected for uniformity
of color. The material manufacturer should supply recommended batch sizes, mixture ratios, mixing methods, and
mixing times.
Mixing equipment can include small electrically powered
mixing blades or specialty units, or resins can be mixed by
hand stirring, if needed. Resin mixing should be in quantities
sufficiently small to ensure that all mixed resin can be used
within the resin’s pot life. Mixed resin that exceeds its pot
life should not be used because the viscosity will continue to
increase and will adversely affect the resin’s ability to
penetrate the surface or saturate the fiber sheet.
6.6—Application of FRP systems
Fumes can accompany the application of some FRP resins.
FRP systems should be selected with consideration for their
440.2R-18
ACI COMMITTEE REPORT
impact on the environment, including emission of volatile
organic compounds and toxicology.
6.6.1 Primer and putty—Where required, primer should be
applied to all areas on the concrete surface where the FRP
system is to be placed. The primer should be placed
uniformly on the prepared surface at the manufacturer’s
specified rate of coverage. The applied primer should be
protected from dust, moisture, and other contaminants
before applying the FRP system.
Putty should be used in an appropriate thickness and
sequence with the primer as recommended by the FRP manufacturer. The system-compatible putty, which is typically a
thickened resin-based paste, should be used only to fill voids
and smooth surface discontinuities before the application of
other materials. Rough edges or trowel lines of cured putty
should be ground smooth before continuing the installation.
Before applying the saturating resin or adhesive, the
primer and putty should be allowed to cure as specified by
the FRP system manufacturer. If the putty and primer are
fully cured, additional surface preparation may be required
before the application of the saturating resin or adhesive.
Surface preparation requirements should be obtained from
the FRP system manufacturer.
6.6.2 Wet layup systems—Wet layup FRP systems are
typically installed by hand using dry fiber sheets and a
saturating resin, typically per the manufacturer’s recommendations. The saturating resin should be applied uniformly to
all prepared surfaces where the system is to be placed. The
fibers can also be impregnated in a separate process using a
resin-impregnating machine before placement on the
concrete surface.
The reinforcing fibers should be gently pressed into the
uncured saturating resin in a manner recommended by the
FRP system manufacturer. Entrapped air between layers
should be released or rolled out before the resin sets.
Sufficient saturating resin should be applied to achieve full
saturation of the fibers.
Successive layers of saturating resin and fiber materials
should be placed before the complete cure of the previous
layer of resin. If previous layers are cured, interlayer surface
preparation, such as light sanding or solvent application as
recommended by the system manufacturer, may be required.
6.6.3 Machine-applied systems—Machine-applied systems
can use resin-preimpregnated tows or dry-fiber tows.
Prepreg tows are impregnated with saturating resin off-site
and delivered to the work site as spools of prepreg tow
material. Dry fibers are impregnated at the job site during
the winding process.
Wrapping machines are primarily used for the automated
wrapping of concrete columns. The tows can be wound
either horizontally or at a specified angle. The wrapping
machine is placed around the column and automatically
wraps the tow material around the perimeter of the column
while moving up and down the column.
After wrapping, prepreg systems should be cured at an
elevated temperature. Usually, a heat source is placed around
the column for a predetermined temperature and time
schedule in accordance with the manufacturer’s recommen-
dations. Temperatures are controlled to ensure consistent
quality. The resulting FRP jackets do not have any seams or
welds because the tows are continuous. In all of the previous
application steps, the FRP system manufacturer’s recommendations should be followed.
6.6.4 Precured systems—Precured systems include shells,
strips, and open grid forms that are typically installed with an
adhesive. Adhesives should be uniformly applied to the
prepared surfaces where precured systems are to be placed,
except in certain instances of concrete confinement where
adhesion of the FRP system to the concrete substrate may not
be required.
Precured laminate surfaces to be bonded should be clean
and prepared in accordance with the manufacturer’s recommendation. The precured sheets or curved shells should be
placed on or into the wet adhesive in a manner recommended
by the FRP manufacturer. Entrapped air between layers
should be released or rolled out before the adhesive sets.
Adhesive should be applied at a rate recommended by the
FRP manufacturer to a minimum concrete surface profile
(CSP) 3 as defined by the ICRI-surface-profile chips to
ensure full bonding of successive layers (ICRI 03732).
6.6.5 NSM systems—NSM systems consist of installing
rectangular or circular FRP bars in grooves cut onto the
concrete surface and bonded in place using an adhesive.
Grooves should be dimensioned to ensure adequate adhesive
around the bars. Figure 13.4 gives typical groove dimensions
for NSM FRP rods and plates. NSM systems can be used on
the topside of structural members and for overhead applications. There are many application methods and types of
adhesive that have been successfully used in the field for
NSM systems. Adhesive type and installation method should
be specified by the NSM system manufacturer.
6.6.6 Protective coatings—Coatings should be compatible
with the FRP strengthening system and applied in accordance
with the manufacturer’s recommendations. Typically, the
use of solvents to clean the FRP surface before installing
coatings is not recommended due to the deleterious effects
that solvents can have on the polymer resins. The FRP
system manufacturer should approve any use of solventwipe preparation of FRP surfaces before the application of
protective coatings.
The coatings should be periodically inspected and maintenance should be provided to ensure the effectiveness of
the coatings.
6.7—Alignment of FRP materials
The FRP-ply orientation and ply-stacking sequence
should be specified. Small variations in angle, as little as 5
degrees, from the intended direction of fiber alignment can
cause a substantial reduction in strength and modulus.
Deviations in ply orientation should only be made if
approved by the licensed design professional.
Sheet and fabric materials should be handled in a manner
to maintain the fiber straightness and orientation. Fabric
kinks, folds, or other forms of severe waviness should be
reported to the licensed design professional.
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
6.8—Multiple plies and lap splices
Multiple plies can be used, provided that all plies are fully
impregnated with the resin system, the resin shear strength is
sufficient to transfer the shearing load between plies, and the
bond strength between the concrete and FRP system is
sufficient. For long spans, multiple lengths of fiber material
or precured stock can be used to continuously transfer the
load by providing adequate lap splices. Lap splices should be
staggered, unless noted otherwise by the licensed design
professional. Lap splice details, including lap length, should
be based on testing and installed in accordance with the
manufacturer’s recommendations. Due to the unique characteristics of some FRP systems, multiple plies and lap splices
are not always possible. Specific guidelines on lap splices
are given in Chapter 13.
6.9—Curing of resins
Curing of resins is a time-temperature-dependent
phenomenon. Ambient-cure resins can take several days to
reach full cure. Temperature extremes or fluctuations can
retard or accelerate the resin curing time. The FRP system
manufacturer may offer several prequalified grades of resin to
accommodate these situations.
Elevated cure systems require the resin to be heated to a
specific temperature for a specified period of time. Various
combinations of time and temperature within a defined
envelope should provide full cure of the system.
All resins should be cured according to the manufacturer’s
recommendation. Field modification of resin chemistry
should not be permitted.
Cure of installed plies should be monitored before placing
subsequent plies. Installation of successive layers should be
halted if there is a curing anomaly.
6.10—Temporary protection
Adverse temperatures; direct contact by rain, dust, or dirt;
excessive sunlight; high humidity; or vandalism can damage
an FRP system during installation and cause improper cure
of the resins. Temporary protection, such as tents and plastic
screens, may be required during installation and until the
resins have cured. If temporary shoring is required, the FRP
system should be fully cured before removing the shoring
and allowing the structural member to carry the design loads.
In the event of suspected damage to the FRP system during
installation, the licensed design professional should be notified
and the FRP system manufacturer consulted.
CHAPTER 7—INSPECTION,
EVALUATION, AND ACCEPTANCE
Quality-assurance and quality-control (QA/QC) programs
and criteria are to be maintained by the FRP system manufacturers, the installation contractors, and others associated with
the project. Quality assurance (QA) is typically an owner or
a licensed professional activity, while quality control (QC) is
a contractor or supplier activity. The QC program should be
comprehensive and cover all aspects of the strengthening
project, and should be detailed in the project specifications
by a licensed professional. The degree of QC and the scope
440.2R-19
of testing, inspection, and record keeping depends on the
size and complexity of the project.
Quality assurance is achieved through a set of inspections
and applicable tests to document the acceptability of the
installation. Project specifications should include a requirement to provide a QA plan for the installation and curing of
all FRP materials. The plan should include personnel safety
issues, application and inspection of the FRP system, location and placement of splices, curing provisions, means to
ensure dry surfaces, QA samples, cleanup, and the required
submittals listed in Section 14.3.
7.1—Inspection
FRP systems and all associated work should be inspected
as required by the applicable codes. In the absence of such
requirements, the inspection should be conducted by or
under the supervision of a licensed design professional or a
qualified inspector. Inspectors should be knowledgeable of
FRP systems and be trained in the installation of FRP
systems. The qualified inspector should require compliance
with the design drawings and project specifications. During
the installation of the FRP system, daily inspection should be
conducted and should include:
• Date and time of installation;
• Ambient temperature, relative humidity, and general
weather observations;
• Surface temperature of concrete;
• Surface dryness per ACI 503.4;
• Surface preparation methods and resulting profile using
the ICRI-surface-profile-chips;
• Qualitative description of surface cleanliness;
• Type of auxiliary heat source, if applicable;
• Widths of cracks not injected with epoxy;
• Fiber or precured laminate batch number(s) and
approximate location in structure;
• Batch numbers, mixture ratios, mixing times, and qualitative descriptions of the appearance of all mixed
resins, including primers, putties, saturants, adhesives,
and coatings mixed for the day;
• Observations of progress of cure of resins;
• Conformance with installation procedures;
• Pull-off test results: bond strength, failure mode, and
location;
• FRP properties from tests of field sample panels or
witness panels, if required;
• Location and size of any delaminations or air voids; and
• General progress of work.
The inspector should provide the licensed design
professional or owner with the inspection records and
witness panels. Records and witness panels should be
retained for a minimum of 10 years or a period specified by
the licensed design professional. The installation contractor
should retain sample cups of mixed resin and maintain a
record of the placement of each batch.
7.2—Evaluation and acceptance
FRP systems should be evaluated and accepted or rejected
based on conformance or nonconformance with the design
440.2R-20
ACI COMMITTEE REPORT
drawings and specifications. FRP system material properties,
installation within specified placement tolerances, presence
of delaminations, cure of resins, and adhesion to substrate
should be included in the evaluation. Placement tolerances
including fiber orientation, cured thickness, ply orientation,
width and spacing, corner radii, and lap splice lengths should
be evaluated.
Witness panel and pulloff tests are used to evaluate the
installed FRP system. In-place load testing can also be used
to confirm the installed behavior of the FRP-strengthened
member (Nanni and Gold 1998).
7.2.1 Materials—Before starting the project, the FRP
system manufacturer should submit certification of specified
material properties and identification of all materials to be
used. Additional material testing can be conducted if deemed
necessary based on the complexity and intricacy of the
project. Evaluation of delivered FRP materials can include
tests for tensile strength, infrared spectrum analysis, Tg, gel
time, pot life, and adhesive shear strength. These tests are
usually performed on material samples sent to a laboratory,
according to the QC test plan. Tests for pot life of resins and
curing hardness are usually conducted on site. Materials that
do not meet the minimum requirements as specified by the
licensed design professional should be rejected.
Witness panels can be used to evaluate the tensile strength
and modulus, lap splice strength, hardness, and Tg of the
FRP system installed and cured on site using installation
procedures similar to those used to install and cure the FRP
system. During installation, flat panels of predetermined
dimensions and thickness can be fabricated on site according
to a predetermined sampling plan. After curing on-site, the
panels can then be sent to a laboratory for testing. Witness
panels can be retained or submitted to an approved laboratory
in a timely manner for testing of strength and Tg. Strength
and elastic modulus of FRP materials can be determined in
accordance with the requirements of Section 4.3.1 and
ACI 440.3R (Test Method L.2) or CSA S806-02. The
properties to be evaluated by testing should be specified.
The licensed design professional may waive or alter the
frequency of testing.
Some FRP systems, including precured and machinewound systems, do not lend themselves to the fabrication of
small, flat, witness panels. For these cases, the licensed
design professional can modify the requirements to include
test panels or samples provided by the manufacturer.
During installation, sample cups of mixed resin should be
prepared according to a predetermined sampling plan and
retained for testing to determine the level of cure (see
Section 7.2.4).
7.2.2 Fiber orientation—Fiber or precured-laminate
orientation should be evaluated by visual inspection. Fiber
waviness—a localized appearance of fibers that deviate from
the general straight-fiber line in the form of kinks or
waves—should be evaluated for wet layup systems.
Fiber or precured laminate misalignment of more than
5 degrees from that specified on the design drawings
(approximately 1 in./ft [80 mm/m]) should be reported to the
licensed design professional for evaluation and acceptance.
7.2.3 Delaminations—The cured FRP system should be
evaluated for delaminations or air voids between multiple
plies or between the FRP system and the concrete. Inspection
methods should be capable of detecting delaminations of 2 in.2
(1300 mm2) or greater. Methods such as acoustic sounding
(hammer sounding), ultrasonics, and thermography can be
used to detect delaminations.
The effect of delaminations or other anomalies on the
structural integrity and durability of the FRP system should
be evaluated. Delamination size, location, and quantity relative
to the overall application area should be considered in the
evaluation.
General acceptance guidelines for wet layup systems are:
• Small delaminations less than 2 in.2 each (1300 mm2)
are permissible as long as the delaminated area is less
than 5% of the total laminate area and there are no more
than 10 such delaminations per 10 ft2 (1 m2);
• Large delaminations, greater than 25 in.2 (16,000 mm2),
can affect the performance of the installed FRP and
should be repaired by selectively cutting away the
affected sheet and applying an overlapping sheet patch
of equivalent plies; and
• Delaminations less than 25 in.2 (16,000 mm2) may be
repaired by resin injection or ply replacement,
depending on the size and number of delaminations and
their locations.
For precured FRP systems, each delamination should be
evaluated and repaired in accordance with the licensed
design professional’s direction. Upon completion of the
repairs, the laminate should be reinspected to verify that the
repair was properly accomplished.
7.2.4 Cure of resins—The relative cure of FRP systems
can be evaluated by laboratory testing of witness panels or
resin-cup samples using ASTM D3418. The relative cure of
the resin can also be evaluated on the project site by physical
observation of resin tackiness and hardness of work surfaces
or hardness of retained resin samples. The FRP system
manufacturer should be consulted to determine the specific
resin-cure verification requirements. For precured systems,
adhesive-hardness measurements should be made in
accordance with the manufacturer’s recommendation.
7.2.5 Adhesion strength—For bond-critical applications,
tension adhesion testing of cored samples should be
conducted using the methods in ACI 503R or ASTM D4541
or the method described by ACI 440.3R, Test Method L.1.
Such tests cannot be performed when using NSM systems.
The sampling frequency should be specified. Tension adhesion
strengths should exceed 200 psi (1.4 MPa), and should
exhibit failure of the concrete substrate. Lower strengths or
failure between the FRP system and the concrete or between
plies should be reported to the licensed design professional
for evaluation and acceptance. For NSM strengthening, sample
cores may be extracted to visually verify the consolidation of
the resin adhesive around the FRP bar. The location of this core
should be chosen such that the continuity of the FRP reinforcement is maintained (that is, at the ends of the NSM bars).
7.2.6 Cured thickness—Small core samples, typically 0.5 in.
(13 mm) in diameter, may be taken to visually ascertain the
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
cured laminate thickness or number of plies. Cored samples
required for adhesion testing also can be used to ascertain the
laminate thickness or number of plies. The sampling
frequency should be specified. Taking samples from highstress areas or splice areas should be avoided. For aesthetic
reasons, the cored hole can be filled and smoothed with a
repair mortar or the FRP system putty. If required, a 4 to 8 in.
(100 to 200 mm) overlapping FRP sheet patch of equivalent
plies may be applied over the filled and smoothed core hole
immediately after taking the core sample. The FRP sheet
patch should be installed in accordance with the manufacturer’s
installation procedures.
CHAPTER 8—MAINTENANCE AND REPAIR
8.1—General
As with any strengthening or retrofit repair, the owner
should periodically inspect and assess the performance of the
FRP system used for strengthening or retrofit repair of
concrete members. The causes of any damage or deficiencies
detected during routine inspections should be identified and
addressed before performing any repairs or maintenance.
8.2—Inspection and assessment
8.2.1 General inspection—A visual inspection looks for
changes in color, debonding, peeling, blistering, cracking,
crazing, deflections, indications of reinforcing-bar corrosion,
and other anomalies. In addition, ultrasonic, acoustic
sounding (hammer tap), or thermographic tests may indicate
signs of progressive delamination.
8.2.2 Testing—Testing can include pull-off tension tests
(Section 7.2.5) or conventional structural loading tests.
8.2.3 Assessment—Test data and observations are used to
assess any damage and the structural integrity of the
strengthening system. The assessment can include a recommendation for repairing any deficiencies and preventing
recurrence of degradation,
8.3—Repair of strengthening system
The method of repair for the strengthening system depends
on the causes of the damage, the type of material, the form of
degradation, and the level of damage. Repairs to the FRP
system should not be undertaken without first identifying
and addressing the causes of the damage.
Minor damage should be repaired, including localized
FRP laminate cracking or abrasions that affect the structural
integrity of the laminate. Minor damage can be repaired by
bonding FRP patches over the damaged area. The FRP
patches should possess the same characteristics, such as
thickness or ply orientation, as the original laminate. The
FRP patches should be installed in accordance with the
material manufacturer’s recommendation. Minor delaminations
can be repaired by resin injection. Major damage, including
peeling and debonding of large areas, may require removal
of the affected area, reconditioning of the cover concrete,
and replacement of the FRP laminate.
8.4—Repair of surface coating
In the event that the surface-protective coating should be
replaced, the FRP laminate should be inspected for structural
440.2R-21
damage or deterioration. The surface coating may be replaced
using a process approved by the system manufacturer.
PART 4—DESIGN RECOMMENDATIONS
CHAPTER 9—GENERAL DESIGN
CONSIDERATIONS
General design recommendations are presented in this
chapter. The recommendations presented are based on the
traditional reinforced concrete design principles stated in the
requirements of ACI 318-05 and knowledge of the specific
mechanical behavior of FRP reinforcement.
FRP strengthening systems should be designed to resist
tensile forces while maintaining strain compatibility between
the FRP and the concrete substrate. FRP reinforcement should
not be relied on to resist compressive forces. It is acceptable,
however, for FRP tension reinforcement to experience
compression due to moment reversals or changes in load
pattern. The compressive strength of the FRP reinforcement,
however, should be neglected.
9.1—Design philosophy
These design recommendations are based on limit-statesdesign principles. This approach sets acceptable levels of
safety for the occurrence of both serviceability limit states
(excessive deflections and cracking) and ultimate limit states
(failure, stress rupture, and fatigue). In assessing the nominal
strength of a member, the possible failure modes and subsequent strains and stresses in each material should be
assessed. For evaluating the serviceability of a member,
engineering principles, such as modular ratios and transformed
sections, can be used.
FRP strengthening systems should be designed in
accordance with ACI 318-05 strength and serviceability
requirements using the strength and load factors stated in
ACI 318-05. Additional reduction factors applied to the
contribution of the FRP reinforcement are recommended by
this guide to reflect uncertainties inherent in FRP systems
compared with steel reinforced and prestressed concrete.
These reduction factors were determined based on statistical
evaluation of variability in mechanical properties, predicted
versus full-scale test results, and field applications. FRP-related
reduction factors were calibrated to produce reliability
indexes typically above 3.5. Reliability indexes between 3.0
and 3.5 can be encountered in cases where relatively low
ratios of steel reinforcement combined with high ratios of
FRP reinforcement are used. Such cases are less likely to be
encountered in design because they violate the strengthincrease limits of Section 9.2. Reliability indexes for FRPstrengthened members are determined based on the approach
used for reinforced concrete buildings (Nowak and Szerszen
2003; Szerszen and Nowak 2003). In general, lower reliability is expected in retrofitted and repaired structures than
in new structures.
9.2—Strengthening limits
Careful consideration should be given to determine
reasonable strengthening limits. These limits are imposed to
guard against collapse of the structure should bond or other
440.2R-22
ACI COMMITTEE REPORT
failure of the FRP system occur due to damage, vandalism,
or other causes. The unstrengthened structural member,
without FRP reinforcement, should have sufficient strength
to resist a certain level of load. In the event that the FRP
system is damaged, the structure will still be capable of
resisting a reasonable level of load without collapse. The
existing strength of the structure should be sufficient to resist
a level of load as described by Eq. (9-1)
(φRn)existing ≥ (1.1SDL + 0.75SLL)new
(9-1)
A dead load factor of 1.1 is used because a relatively accurate
assessment of the existing dead loads of the structure can be
determined. A live load factor of 0.75 is used to exceed the
statistical mean of yearly maximum live load factor of 0.5, as
given in ASCE 7-05. The minimum strengthening limit of
Eq. (9-1) will allow the strengthened member to maintain
sufficient structural capacity until the damaged FRP has
been repaired.
In cases where the design live load acting on the member
to be strengthened has a high likelihood of being present for
a sustained period of time, a live load factor of 1.0 should be
used instead of 0.75 in Eq. (9-1). Examples include library
stack areas, heavy storage areas, warehouses, and other
occupancies with a live load exceeding 150 lb/ft2 (730 kg/m2).
More specific limits for structures requiring a fire endurance
rating are given in Section 9.2.1.
9.2.1 Structural fire endurance—The level of strengthening
that can be achieved through the use of externally bonded FRP
reinforcement is often limited by the code-required fireresistance rating of a structure. The polymer resins currently
used in wet layup and prepreg FRP systems and the polymer
adhesives used in precured FRP systems suffer deterioration
of mechanical and bond properties at temperatures close to
or exceeding the Tg of the polymer (Bisby et al. 2005b).
While the Tg can vary significantly, depending on the
polymer chemistry, a typical range for field-applied resins
and adhesives is 140 to 180 °F (60 to 82 °C).
Although the FRP system itself has a low fire endurance,
a combination of the FRP system with an existing concrete
structure may still have an adequate level of fire endurance.
This occurs because an insulation system can improve the
overall fire rating of a reinforced concrete member by
providing protection to its components, concrete, and
reinforcing steel. The insulation system can delay strength
degradation of the concrete and steel due to fire exposure and
increase their residual strengths, thus increasing the fire
rating of the member. Hence, with proper insulation, the fire
rating of a member can be increased even with the FRP
contribution ignored (Bisby et al. 2005a; Williams et al.
2006). This is attributable to the inherent fire endurance of
the existing concrete structure alone. To investigate the fire
endurance of an FRP-strengthened concrete structure, it is
important to recognize that the strength of traditional reinforced
concrete structures is somewhat reduced during exposure to
the high temperatures associated with a fire event as well.
The yield strength of reinforcing steel and the compressive
strength of concrete are reduced. As a result, the overall
resistance of a reinforced concrete member to load effects is
reduced. This concept is used in ACI 216R to provide a
method of computing the fire endurance of concrete
members. ACI 216R suggests limits that maintain a reasonable
level of safety against complete collapse of the structure in
the event of a fire.
By extending the concepts established in ACI 216R to
FRP-strengthened reinforced concrete, limits on strengthening
can be used to ensure a strengthened structure will not
collapse in a fire event. A member’s resistance to load
effects, with reduced steel and concrete strengths and
without the strength of the FRP reinforcement, can be
computed. This resistance can then be compared with the
load demand on the member to ensure the structure will not
collapse under service loads and elevated temperatures.
The nominal strength of a structural member with a fire
resistance rating should satisfy the conditions of Eq. (9-2) if
it is to be strengthened with an FRP system. The load effects,
SDL and SLL, should be determined using the current load
requirements for the structure. If the FRP system is meant to
allow greater load-carrying strength, such as an increase in
live load, the load effects should be computed using these
greater loads. The nominal strength at high temperature
should be greater than the strengthened service load on the
member (ACI 216R should be used for ASTM E119 fire
scenarios)
Rnθ ≥ SDL + SLL
(9-2)
The nominal resistance of the member at an elevated
temperature Rnθ may be determined using the guidelines
outlined in ACI 216R or through testing. The nominal
resistance Rnθ should be calculated based on the reduced
properties of the existing member. The resistance should be
computed for the time period required by the structure’s fireresistance rating—for example, a 2-hour fire rating—and
should not account for the contribution of the FRP system,
unless the FRP temperature can be demonstrated to remain
below a critical temperature for FRP. The critical temperature
for the FRP may be defined as the temperature at which
significant deterioration of FRP properties has occurred.
More research is needed to accurately identify critical
temperatures for different types of FRP. Until better information on the properties of FRP at high temperature is
available, the critical temperature of an FRP strengthening
system can be taken as the lowest Tg of the components of
the system.
Furthermore, if the FRP system is meant to address a loss
in strength, such as deterioration, the resistance should
reflect this loss. The fire endurance of FRP materials and
FRP strengthening systems can be improved through the use
of polymers having high Tg or using fire protection (Bisby et
al. 2005a).
9.2.2 Overall structural strength—While FRP systems are
effective in strengthening members for flexure and shear and
providing additional confinement, other modes of failure,
such as punching shear and bearing capacity of footings,
may be only slightly affected by FRP systems (Sharaf et al.
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
2006). All members of a structure should be capable of withstanding the anticipated increase in loads associated with the
strengthened members.
Additionally, analysis should be performed on the
member strengthened by the FRP system to check that under
overload conditions the strengthened member will fail in a
flexural mode rather than in a shear mode.
9.2.3 Seismic applications—The majority of research into
seismic strengthening of structures has dealt with strengthening
of columns. FRP systems confine columns to improve
concrete compressive strength, reduce required splice
length, and increase the shear strength (Priestley et al. 1996).
Limited information is available for strengthening building
frames in seismic zones. When beams or floors in building
frames in seismic zones are strengthened, the strength and
stiffness of both the beam/floor and column should be
checked to ensure the formation of the plastic hinge away
from the column and the joint (Mosallam et al. 2000).
9.3—Selection of FRP systems
9.3.1 Environmental considerations—Environmental
conditions uniquely affect resins and fibers of various FRP
systems. The mechanical properties (for example, tensile
strength, ultimate tensile strain, and elastic modulus) of
some FRP systems degrade under exposure to certain
environments, such as alkalinity, salt water, chemicals,
ultraviolet light, high temperatures, high humidity, and
freezing-and-thawing cycles. The material properties used in
design should account for this degradation in accordance
with Section 9.4.
The licensed design professional should select an FRP
system based on the known behavior of that system in the
anticipated service conditions. Some important environmental
considerations that relate to the nature of the specific
systems are given as follows. Specific information can be
obtained from the FRP system manufacturer.
• Alkalinity/acidity—The performance of an FRP system
over time in an alkaline or acidic environment depends
on the matrix material and the reinforcing fiber. Dry,
unsaturated bare, or unprotected carbon fiber is resistant
to both alkaline and acidic environments, while bare
glass fiber can degrade over time in these environments. A properly applied resin matrix, however,
should isolate and protect the fiber from the alkaline/
acidic environment and retard deterioration. The FRP
system selected should include a resin matrix resistant to
alkaline and acidic environments. Sites with high alkalinity and high moisture or relative humidity favor the
selection of carbon-fiber systems over glass-fiber systems;
• Thermal expansion—FRP systems may have thermal
expansion properties that are different from those of
concrete. In addition, the thermal expansion properties
of the fiber and polymer constituents of an FRP system
can vary. Carbon fibers have a coefficient of thermal
expansion near zero whereas glass fibers have a coefficient
of thermal expansion similar to concrete. The polymers
used in FRP strengthening systems typically have
coefficients of thermal expansion roughly five times
440.2R-23
that of concrete. Calculation of thermally-induced
strain differentials are complicated by variations in
fiber orientation, fiber volume fraction (ratio of the
volume of fibers to the volume of fibers and resins in an
FRP), and thickness of adhesive layers. Experience
(Motavalli et al. 1997; Soudki and Green 1997; Green
et al. 1998) indicates, however, that thermal expansion
differences do not affect bond for small ranges of
temperature change, such as ±50 °F (±28 °C); and
• Electrical conductivity—GFRP and AFRP are effective
electrical insulators, whereas CFRP is conductive. To
avoid potential galvanic corrosion of steel elements,
carbon-based FRP materials should not come in direct
contact with steel.
9.3.2 Loading considerations—Loading conditions
uniquely affect different fibers of FRP systems. The licensed
design professional should select an FRP system based on
the known behavior of that system in the anticipated service
conditions.
Some important loading considerations that relate to the
nature of the specific systems are given below. Specific
information should be obtained from material manufacturers.
• Impact tolerance—AFRP and GFRP systems demonstrate
better tolerance to impact than CFRP systems; and
• Creep-rupture and fatigue—CFRP systems are highly
resistive to creep-rupture under sustained loading and
fatigue failure under cyclic loading. GFRP systems are
more sensitive to both loading conditions.
9.3.3 Durability considerations—Durability of FRP
systems is the subject of considerable ongoing research
(Steckel et al. 1999). The licensed design professional
should select an FRP system that has undergone durability
testing consistent with the application environment. Durability
testing may include hot-wet cycling, alkaline immersion,
freezing-and-thawing cycling, ultraviolet exposure, dry heat,
and salt water.
Any FRP system that completely encases or covers a
concrete section should be investigated for the effects of a
variety of environmental conditions including those of
freezing and thawing, steel corrosion, alkali and silica aggregate
reactions, water entrapment, vapor pressures, and moisture
vapor transmission (Masoud and Soudki 2006; Soudki and
Green 1997; Porter et al. 1997; Christensen et al. 1996;
Toutanji 1999). Many FRP systems create a moistureimpermeable layer on the surface of the concrete. In areas
where moisture vapor transmission is expected, adequate
means should be provided to allow moisture to escape from
the concrete structure.
9.3.4 Protective-coating selection considerations—A
coating or insulation system can be applied to the installed
FRP system to protect it from exposure to certain environmental conditions (Bisby et al. 2005a; Williams et al. 2006).
The thickness and type of coating should be selected based
on the requirements of the composite repair; resistance to
environmental effects such as moisture, salt water, temperature
extremes, fire, impact, and UV exposure; resistance to sitespecific effects; and resistance to vandalism. Coatings are
relied on to retard the degradation of the mechanical properties
440.2R-24
ACI COMMITTEE REPORT
Table 9.1—Environmental reduction factor for
various FRP systems and exposure conditions
Exposure conditions
Environmental
Fiber type reduction factor CE
Interior exposure
Carbon
Glass
0.95
0.75
Aramid
Carbon
0.85
0.85
Exterior exposure (bridges, piers, and
unenclosed parking garages)
Aggressive environment (chemical
plants and wastewater treatment plants)
Glass
0.65
Aramid
0.75
Carbon
Glass
0.85
0.50
Aramid
0.70
of the FRP systems. The coatings should be periodically
inspected and maintained to ensure the effectiveness of the
coatings.
External coatings or thickened coats of resin over fibers
can protect them from damage due to impact or abrasion. In
high-impact or traffic areas, additional levels of protection
may be necessary. Portland-cement plaster and polymer
coatings are commonly used for protection where minor
impact or abrasion is anticipated.
9.4—Design material properties
Unless otherwise stated, the material properties reported
by manufacturers, such as the ultimate tensile strength,
typically do not consider long-term exposure to environmental
conditions and should be considered as initial properties.
Because long-term exposure to various types of environments
can reduce the tensile properties and creep-rupture and
fatigue endurance of FRP laminates, the material properties
used in design equations should be reduced based on the
environmental exposure condition.
Equations (9-3) through (9-5) give the tensile properties
that should be used in all design equations. The design ultimate
tensile strength should be determined using the environmental
reduction factor given in Table 9.1 for the appropriate fiber
type and exposure condition
ffu = CE ffu*
(9-3)
Similarly, the design rupture strain should also be reduced
for environmental exposure conditions
εfu = CEεfu*
(9-4)
Because FRP materials are linear elastic until failure, the
design modulus of elasticity for unidirectional FRP can be
determined from Hooke’s law. The expression for the
modulus of elasticity, given in Eq. (9-5), recognizes that the
modulus is typically unaffected by environmental conditions.
The modulus given in this equation will be the same as the
initial value reported by the manufacturer
Ef = ffu /εfu
(9-5)
The constituent materials, fibers, and resins of an FRP
system affect its durability and resistance to environmental
exposure. The environmental reduction factors given in
Table 9.1 are conservative estimates based on the relative
durability of each fiber type. As more research information
is developed and becomes available, these values will be
refined. The methodology regarding the use of these factors,
however, will remain unchanged. When available, durability
test data for FRP systems with and without protective coatings
may be obtained from the manufacturer of the FRP system
under consideration.
As Table 9.1 illustrates, if the FRP system is located in a
relatively benign environment, such as indoors, the reduction
factor is closer to unity. If the FRP system is located in an
aggressive environment where prolonged exposure to high
humidity, freezing-and-thawing cycles, salt water, or alkalinity
is expected, a lower reduction factor should be used. The
reduction factor can reflect the use of a protective coating if
the coating has been shown through testing to lessen the
effects of environmental exposure and the coating is
maintained for the life of the FRP system.
CHAPTER 10—FLEXURAL STRENGTHENING
Bonding FRP reinforcement to the tension face of a
concrete flexural member with fibers oriented along the
length of the member will provide an increase in flexural
strength. Increases in overall flexural strength from 10 to
160% have been documented (Meier and Kaiser 1991;
Ritchie et al. 1991; Sharif et al. 1994). When taking into
account the strengthening limits of Section 9.2 and ductility
and serviceability limits, however, strength increases of up
to 40% are more reasonable.
This chapter does not apply to FRP systems used to
enhance the flexural strength of members in the expected
plastic hinge regions of ductile moment frames resisting
seismic loads. The design of such applications, if used,
should examine the behavior of the strengthened frame,
considering that the strengthened sections have muchreduced rotation and curvature capacities. In this case, the
effect of cyclic load reversal on the FRP reinforcement
should be investigated.
10.1—Nominal strength
The strength design approach requires that the design flexural
strength of a member exceed its required factored moment as
indicated by Eq. (10-1). The design flexural strength φMn
refers to the nominal strength of the member multiplied by a
strength reduction factor, and the factored moment Mu refers
to the moment calculated from factored loads (for example,
αDLMDL + αLLMLL +...)
φMn ≥ Mu
(10-1)
This guide recommends that the factored moment Mu of a
section be calculated by use of load factors as required by
ACI 318-05. In addition, an additional strength reduction
factor for FRP, ψf , should be applied to the flexural contribution
of the FRP reinforcement alone, Mnf , as described in Section
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
440.2R-25
Fig. 10.1—Debonding and delamination of externally bonded FRP systems.
10.2.10. The additional strength reduction factor, ψf , is used
to improve the reliability of strength prediction and accounts
for the different failure modes observed for FRP-strengthened
members (delamination of FRP reinforcement).
The nominal flexural strength of FRP-strengthened
concrete members with mild steel reinforcement and with
bonded prestressing steel can be determined based on strain
compatibility, internal force equilibrium, and the controlling
mode of failure. For members with unbonded prestressed
steel, strain compatibility does not apply and the stress in the
unbonded tendons at failure depends on the overall deformation
of the member and is assumed to be approximately the same
at all sections. No specific guidelines on FRP strengthening
of concrete members with unbonded prestressing steel are
provided at this time.
10.1.1 Failure modes—The flexural strength of a section
depends on the controlling failure mode. The following flexural
failure modes should be investigated for an FRP-strengthened
section (GangaRao and Vijay 1998):
• Crushing of the concrete in compression before
yielding of the reinforcing steel;
• Yielding of the steel in tension followed by rupture of
the FRP laminate;
• Yielding of the steel in tension followed by concrete
crushing;
• Shear/tension delamination of the concrete cover (cover
delamination); and
• Debonding of the FRP from the concrete substrate
(FRP debonding).
Concrete crushing is assumed to occur if the compressive
strain in the concrete reaches its maximum usable strain (εc =
εcu = 0.003). Rupture of the externally bonded FRP is
assumed to occur if the strain in the FRP reaches its design
rupture strain (εf = εfu) before the concrete reaches its
maximum usable strain.
Cover delamination or FRP debonding can occur if the force
in the FRP cannot be sustained by the substrate (Fig. 10.1).
Such behavior is generally referred to as debonding, regardless
of where the failure plane propagates within the FRP-adhesivesubstrate region. Guidance to avoid the cover delamination
failure mode is given in Chapter 13.
Away from the section where externally bonded FRP
terminates, a failure controlled by FRP debonding may
govern (Fig. 10.1(b)). To prevent such an intermediate
crack-induced debonding failure mode, the effective strain in
FRP reinforcement should be limited to the strain level at
which debonding may occur, εfd, as defined in Eq. (10-2)
f c′
ε fd = 0.083 ----------≤ 0.9ε fu in in.-lb units
nE f t f
f c′
ε fd = 0.41 ----------≤ 0.9ε fu in SI units
nE f t f
(10-2)
Equation (10-2) takes a modified form of the debonding
strain equation proposed by Teng et al. (2001, 2004) that was
based on committee evaluation of a significant database for
flexural beam tests exhibiting FRP debonding failure. The
proposed equation was calibrated using average measured
values of FRP strains at debonding and the database for flexural
tests experiencing intermediate crack-induced debonding to
determine the best fit coefficient of 0.083 (0.41 in SI units).
Reliability of FRP contribution to flexural strength is
addressed by incorporating an additional strength reduction
factor for FRP ψf in addition to the strength reduction factor
φ per ACI 318-05 for structural concrete.
Transverse clamping with FRP layers improves bond
behavior relative to that predicted by Eq. (10-2). Provision of
transverse clamping FRP U-wraps along the length of the
flexural FRP reinforcement has been observed to result in
increased FRP strain at debonding. An improvement of up to
30% increase in debonding strain has been observed
(CECS-146 (2003)). Further research is needed to understand
440.2R-26
ACI COMMITTEE REPORT
the influence of transverse FRP on the debonding strain of
longitudinal FRP.
For NSM FRP applications, the value of εfd may vary from
0.6εfu to 0.9εfu depending on many factors such as member
dimensions, steel and FRP reinforcement ratios, and surface
roughness of the FRP bar. Based on existing studies (Hassan
and Rizkalla 2003; De Lorenzis et al. 2004; Kotynia 2005),
the committee recommends the use of εfd = 0.7εfu. To
achieve the debonding design strain of NSM FRP bars εfd,
the bonded length should be greater than the development
length given in Chapter 13.
10.2—Reinforced concrete members
This section presents guidance on the calculation of the
flexural strengthening effect of adding longitudinal FRP
reinforcement to the tension face of a reinforced concrete
member. A specific illustration of the concepts in this section
applied to strengthening of existing rectangular sections
reinforced in the tension zone with nonprestressed steel is
given. The general concepts outlined herein can, however, be
extended to nonrectangular shapes (T-sections and I-sections)
and to members with compression steel reinforcement.
10.2.1 Assumptions—The following assumptions are
made in calculating the flexural resistance of a section
strengthened with an externally applied FRP system:
• Design calculations are based on the dimensions,
internal reinforcing steel arrangement, and material
properties of the existing member being strengthened;
• The strains in the steel reinforcement and concrete are
directly proportional to the distance from the neutral
axis. That is, a plane section before loading remains
plane after loading;
• There is no relative slip between external FRP reinforcement and the concrete;
• The shear deformation within the adhesive layer is
neglected because the adhesive layer is very thin with
slight variations in its thickness;
• The maximum usable compressive strain in the
concrete is 0.003;
• The tensile strength of concrete is neglected; and
• The FRP reinforcement has a linear elastic stress-strain
relationship to failure.
While some of these assumptions are necessary for the
sake of computational ease, the assumptions do not accurately
reflect the true fundamental behavior of FRP flexural
reinforcement. For example, there will be shear deformation
in the adhesive layer causing relative slip between the FRP
and the substrate. The inaccuracy of the assumptions will
not, however, significantly affect the computed flexural
strength of an FRP-strengthened member. An additional
strength reduction factor (presented in Section 10.2.10) will
conservatively compensate for any such discrepancies.
10.2.2 Shear strength—When FRP reinforcement is being
used to increase the flexural strength of a member, the
member should be capable of resisting the shear forces
associated with the increased flexural strength. The potential
for shear failure of the section should be considered by
comparing the design shear strength of the section to the
required shear strength. If additional shear strength is
required, FRP laminates oriented transverse to the beam
longitudinal axis can be used to resist shear forces as
described in Chapter 11.
10.2.3 Existing substrate strain—Unless all loads on a
member, including self-weight and any prestressing forces,
are removed before installation of FRP reinforcement, the
substrate to which the FRP is applied will be strained. These
strains should be considered as initial strains and should be
excluded from the strain in the FRP (Arduini and Nanni
1997; Nanni and Gold 1998). The initial strain level on the
bonded substrate, εbi, can be determined from an elastic
analysis of the existing member, considering all loads that
will be on the member during the installation of the FRP
system. The elastic analysis of the existing member should
be based on cracked section properties.
10.2.4 Flexural strengthening of concave soffits—The
presence of curvature in the soffit of a concrete member may
lead to the development of tensile stresses normal to the
adhesive and surface to which the FRP is bonded. Such
tensile stresses result when the FRP tends to straighten under
load, and can promote the initiation of FRP laminate separation
failure that reduces the effectiveness of the FRP flexural
strengthening (Aiello et al. 2001; Eshwar et al. 2003). If the
extent of the curved portion of the soffit exceeds a length of
40 in. (1.0 m) with a rise of 0.2 in. (5 mm), the surface should
be made flat before strengthening. Alternately, anchor
systems such as FRP anchors or U-wraps should be installed
to prevent delamination (Eshwar et al. 2003).
10.2.5 Strain level in FRP reinforcement—It is important
to determine the strain level in the FRP reinforcement at the
ultimate limit state. Because FRP materials are linear elastic
until failure, the level of strain in the FRP will dictate the
level of stress developed in the FRP. The maximum strain
level that can be achieved in the FRP reinforcement will be
governed by either the strain level developed in the FRP at
the point at which concrete crushes, the point at which the
FRP ruptures, or the point at which the FRP debonds from
the substrate. The effective strain level in the FRP reinforcement at the ultimate limit state can be found from Eq. (10-3)
d f – c⎞
ε fe = ε cu ⎛ ------------ – ε bi ≤ ε fd
⎝ c ⎠
(10-3)
where εbi is the initial substrate strain as described in Section
10.2.3, and df is the effective depth of FRP reinforcement, as
indicated in Fig. 10.2.
10.2.6 Stress level in the FRP reinforcement—The effective
stress level in the FRP reinforcement is the maximum level
of stress that can be developed in the FRP reinforcement
before flexural failure of the section. This effective stress
level can be found from the strain level in the FRP, assuming
perfectly elastic behavior
ffe = Ef εfe
(10-4)
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
440.2R-27
Fig. 10.2—Effective depth of FRP systems.
10.2.7 Strength reduction factor—The use of externally
bonded FRP reinforcement for flexural strengthening will
reduce the ductility of the original member. In some cases, the
loss of ductility is negligible. Sections that experience a significant loss in ductility, however, should be addressed. To maintain a sufficient degree of ductility, the strain level in the steel at
the ultimate limit state should be checked. For reinforced
concrete members with nonprestressed steel reinforcement,
adequate ductility is achieved if the strain in the steel at the point
of concrete crushing or failure of the FRP, including delamination or debonding, is at least 0.005, according to the definition
of a tension-controlled section as given in ACI 318-05.
The approach taken by this guide follows the philosophy
of ACI 318-05. A strength reduction factor given by Eq. (10-5)
should be used, where εt is the net tensile strain in extreme
tension steel at nominal strength, as defined in ACI 318-05
⎧0.90 for ε t ≥ 0.005
⎪
0.25 ( ε t – ε sy )
⎪
φ = ⎨ 0.65 + ------------------------------- for ε sy < ε t < 0.005
0.005 – ε sy
⎪
⎪
⎩ 0.65 for ε t ≤ ε sy
(10-5)
This equation sets the reduction factor at 0.90 for ductile
sections and 0.65 for brittle sections where the steel does not
yield, and provides a linear transition for the reduction factor
between these two extremes (Fig. 10.3).
10.2.8 Serviceability—The serviceability of a member
(deflections and crack widths) under service loads should
satisfy applicable provisions of ACI 318-05. The effect of
the FRP external reinforcement on the serviceability can be
assessed using the transformed-section analysis.
To avoid inelastic deformations of reinforced concrete
members with nonprestressed steel reinforcement strengthened
with external FRP reinforcement, the existing internal steel
reinforcement should be prevented from yielding under
service load levels, especially for members subjected to
cyclic loads (El-Tawil et al. 2001). The stress in the steel
reinforcement under service load should be limited to 80%
of the yield strength, as shown in Eq. (10-6). In addition,
the compressive stress in concrete under service load
should be limited to 45% of the compressive strength, as
shown in Eq. (10-7)
Fig. 10.3—Graphical representation of strength reduction
factor.
Fig. 10.4—Illustration of the level of applied moment to be
used to check the stress limits in the FRP reinforcement.
fs,s ≤ 0.80fy
(10-6)
fc,s ≤ 0.45fc′
(10-7)
10.2.9 Creep-rupture and fatigue stress limits—To avoid
creep-rupture of the FRP reinforcement under sustained
stresses or failure due to cyclic stresses and fatigue of the FRP
reinforcement, the stress levels in the FRP reinforcement
under these stress conditions should be checked. Because
these stress levels will be within the elastic response range of
the member, the stresses can be computed by elastic analysis.
In Section 4.4, the creep-rupture phenomenon and fatigue
characteristics of FRP material were described and the resistance to its effects by various types of fibers was examined.
As stated in Section 4.4.1, research has indicated that glass,
aramid, and carbon fibers can sustain approximately 0.3, 0.5,
and 0.9 times their ultimate strengths, respectively, before
encountering a creep-rupture problem (Yamaguchi et al.
1997; Malvar 1998). To avoid failure of an FRP-reinforced
member due to creep-rupture and fatigue of the FRP, stress
limits for these conditions should be imposed on the FRP
reinforcement. The stress level in the FRP reinforcement can
be computed using elastic analysis and an applied moment
due to all sustained loads (dead loads and the sustained
portion of the live load) plus the maximum moment induced
in a fatigue loading cycle (Fig. 10.4). The sustained stress
440.2R-28
ACI COMMITTEE REPORT
Fig. 10.5—Internal strain and stress distribution for a rectangular section under flexure at
ultimate limit state.
Table 10.1—Sustained plus cyclic service load
stress limits in FRP reinforcement
Fiber type
Stress type
Sustained plus
cyclic stress limit
GFRP
AFRP
CFRP
0.20ffu
0.30ffu
0.55ffu
should be limited as expressed by Eq. (10-8) to maintain
safety. Values for safe sustained plus cyclic stress levels are
given in Table 10.1. These values are based approximately
on the stress limits previously stated in Section 4.4.1 with an
imposed safety factor of 1/0.6
ff,s ≤ sustained plus cyclic stress limit
(10-8)
10.2.10 Ultimate strength of singly reinforced rectangular
section—To illustrate the concepts presented in this chapter,
this section describes the application of these concepts to a
singly-reinforced rectangular section (nonprestressed).
Figure 10.5 illustrates the internal strain and stress distribution
for a rectangular section under flexure at the ultimate limit state.
The calculation procedure used to arrive at the ultimate
strength should satisfy strain compatibility and force
equilibrium and should consider the governing mode of
failure. Several calculation procedures can be derived to
satisfy these conditions. The calculation procedure described
herein illustrates a trial-and-error method.
The trial-and-error procedure involves selecting an
assumed depth to the neutral axis c; calculating the strain
level in each material using strain compatibility; calculating
the associated stress level in each material; and checking
internal force equilibrium. If the internal force resultants do
not equilibrate, the depth to the neutral axis should be revised
and the procedure repeated.
For any assumed depth to the neutral axis c, the strain level
in the FRP reinforcement can be computed from Eq. (10-3)
presented in Section 10.2.5 and reprinted below for convenience. This equation considers the governing mode of failure
for the assumed neutral axis depth. If the left term of the
inequality controls, concrete crushing controls flexural
failure of the section. If the right term of the inequality
controls, FRP failure (rupture or debonding) controls flexural
failure of the section
d f – c⎞
ε fe = ε cu ⎛ ------------ – ε bi ≤ ε fd
⎝ c ⎠
(10-3)
The effective stress level in the FRP reinforcement can be
found from the strain level in the FRP, assuming perfectly
elastic behavior
ffe = Ef εfe
(10-9)
Based on the strain level in the FRP reinforcement, the
strain level in the nonprestressed steel reinforcement can be
found from Eq. (10-10) using strain compatibility
d–c
εs = (εfe + εbi) ⎛ -------------⎞
⎝ d f – c⎠
(10-10)
The stress in the steel is determined from the strain level
in the steel using its stress-strain curve
fs = Esεs ≤ fy
(10-11)
With the strain and stress level in the FRP and steel
reinforcement determined for the assumed neutral axis depth,
internal force equilibrium may be checked using Eq. (10-12)
A s f s + A f f fe
c = ------------------------α 1 f c′ β 1 b
(10-12)
The terms α1 and β1 in Eq. (10-12) are parameters
defining a rectangular stress block in the concrete equivalent
to the nonlinear distribution of stress. If concrete crushing is
the controlling mode of failure (before or after steel yielding),
α1 and β1 can be taken as the values associated with the
Whitney stress block (α1 = 0.85 and β1 from Section
10.2.7.3 of ACI 318-05). If FRP rupture, cover delamination,
or FRP debonding occur, the Whitney stress block will give
reasonably accurate results. A more accurate stress block for
the strain level reached in the concrete at the ultimate-limit
state may be used. Moreover, methods considering a
nonlinear stress distribution in the concrete can also be used.
The depth to the neutral axis c is found by simultaneously
satisfying Eq. (10-3), (10-9), (10-10), (10-11), and (10-12),
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
440.2R-29
Fig. 10.6—Elastic strain and stress distribution.
thus establishing internal force equilibrium and strain
compatibility. To solve for the depth of the neutral axis, c, an
iterative solution procedure can be used. An initial value for
c is first assumed and the strains and stresses are calculated
using Eq. (10-3), (10-9), (10-10), and (10-11). A revised value
for the depth of neutral axis c is then calculated from Eq. (10-12).
The calculated and assumed values for c are then compared.
If they agree, then the proper value of c is reached. If the
calculated and assumed values do not agree, another value
for c is selected, and the process is repeated until convergence
is attained.
The nominal flexural strength of the section with FRP
external reinforcement is computed from Eq. (10-13). An
additional reduction factor for FRP, ψf , is applied to the
flexural-strength contribution of the FRP reinforcement.
The recommended value of ψf is 0.85. This reduction factor
for the strength contribution of FRP reinforcement is based
on the reliability analysis discussed in Section 9.1, which
was based on the experimentally calibrated statistical
properties of the flexural strength (Okeil et al. 2007)
β 1 c⎞
β 1 c⎞
Mn = As fs ⎛ d ------- + ψ f A f f fe ⎛ h ------⎝ 2 ⎠
⎝ 2 ⎠
(10-13)
10.2.10.1 Stress in steel under service loads—The stress
level in the steel reinforcement can be calculated based on a
cracked-section analysis of the FRP-strengthened reinforced
concrete section, as indicated by Eq. (10-14)
kd
M s + ε bi A f E f ⎛ d f – ------⎞ ( d – kd )E s
⎝
3⎠
f s, s = ----------------------------------------------------------------------------------------------------------------kd
A s E s ⎛ d – kd
------⎞ ( d – kd ) + A f E f ⎛ d f – ------⎞ ( d f – kd )
⎝
⎝
3⎠
3⎠
(10-14)
The distribution of strain and stress in the reinforced
concrete section is shown in Fig. 10.6. Similar to conventional
reinforced concrete, the depth to the neutral axis at service,
kd, can be computed by taking the first moment of the areas
of the transformed section. The transformed area of the FRP
may be obtained by multiplying the area of FRP by the
modular ratio of FRP to concrete. Although this method
ignores the difference in the initial strain level of the FRP,
the initial strain level does not greatly influence the depth to
the neutral axis in the elastic response range of the member.
The stress in the steel under service loads computed from
Eq. (10-14) should be compared against the limits described
in Section 10.2.8: Ms from Eq. (10-14) equal to the moment
due to all sustained loads (dead loads and the sustained
portion of the live load) plus the maximum moment induced
in a fatigue loading cycle, as shown in Fig. 10.4.
10.2.10.2 Stress in FRP under service loads—The stress
level in the FRP reinforcement can be computed using
Eq. (10-15) with fs,s from Eq. (10-14). Equation (10-15) gives
the stress level in the FRP reinforcement under an applied
moment within the elastic response range of the member
E d f – kd
f f, s = f s, s ⎛ -----f ⎞ --------------- – ε bi E f
⎝ E s⎠ d – kd
(10-15)
The stress in the FRP under service loads computed from
Eq. (10-15) should be compared against the limits described
in Section 10.2.9.
10.3—Prestressed concrete members
This section presents guidance on the effect of adding
longitudinal FRP reinforcement to the tension face of a
rectangular prestressed concrete member. The general
concepts outlined herein can be extended to nonrectangular
shapes (T-sections and I-sections) and to members with
tension and/or compression nonprestressed steel reinforcement.
10.3.1 Members with bonded prestressing steel
10.3.1.1 Assumptions—In addition to the basic assumptions
for concrete and FRP behavior for a reinforced concrete
section listed in Section 10.2.1, the following assumptions
are made in calculating the flexural resistance of a
prestressed section strengthened with an externally applied
FRP system:
• Strain compatibility can be used to determine strain in
the externally bonded FRP, strain in the nonprestressed
steel reinforcement, and the strain or strain change in
the prestressing steel;
• Additional flexural failure mode controlled by
prestressing steel rupture should be investigated;
• For cases where the prestressing steel is draped, several
sections along the span of the member should be evaluated
to verify strength requirements; and
• The initial strain level of the concrete substrate εbi
should be calculated and excluded from the effective
440.2R-30
ACI COMMITTEE REPORT
strain in the FRP. The initial strain can be determined
from an elastic analysis of the existing member,
considering all loads that will be on the member at the
time of FRP installation. Analysis should be based on
the actual condition of the member (cracked or uncracked
section) to determine the substrate initial strain level.
10.3.1.2 Strain in FRP reinforcement—The maximum
strain that can be achieved in the FRP reinforcement will be
governed by strain limitations due to either concrete
crushing, FRP rupture, FRP debonding, or prestressing steel
rupture. The effective design strain for FRP reinforcement at
the ultimate-limit state for failure controlled by concrete
crushing can be calculated by use of Eq. (10-16)
d f – c⎞
ε fe = ε cu ⎛ ------------ – ε bi ≤ ε fd
⎝ c ⎠
(10-16)
For failure controlled by prestressing steel rupture,
Eq. (10-17) and (10-18) can be used. For Grade 270 and 250 ksi
(1860 and 1725 MPa) strand, the value of εpu to be used in
Eq. (10-17) is 0.035
df – c ⎞
ε fe = ( ε pu – ε pi ) ⎛ ------------- – ε bi ≤ ε fd
⎝ d p – c⎠
(10-17)
in which
2
Pe
Pe ⎛
e⎞
ε pi = ----------- + ----------⎜ 1 + ----2⎟
Ap Ep Ac Ec ⎝
r ⎠
(10-18)
10.3.1.3 Strength reduction factor—To maintain a
sufficient degree of ductility, the strain in the prestressing
steel at the nominal strength should be checked. Adequate
ductility is achieved if the strain in the prestressing steel at
the nominal strength is at least 0.013. Where this strain
cannot be achieved, the strength reduction factor is decreased
to account for a less ductile failure. The strength reduction
factor for a member prestressed with standard 270 and 250 ksi
(1860 and 1725 MPa) prestressing steel is given by Eq. (10-19),
where εps is the prestressing steel strain at the nominal strength
⎧ 0.90 for ε ps ≥ 0.013
⎪
⎪
0.25 ( ε ps – 0.010 )
φ = ⎨ 0.65 + ----------------------------------------for 0.010 < ε ps < 0.013
0.013 – 0.010
⎪
⎪ 0.65 for ε ≤ 0.010
ps
⎩
(10-19)
10.3.1.4 Serviceability—To avoid inelastic deformations
of the strengthened member, the prestressing steel should be
prevented from yielding under service load levels. The stress in
the steel under service load should be limited per Eq. (10-20). In
addition, the compressive stress in the concrete under service
load should be limited to 45% of the compressive strength
fps,s ≤ 0.82fpy
(10-20a)
fps,s ≤ 0.74fpu
(10-20b)
When fatigue is a concern (for example, in bridges), the
stress in the prestressing steel due to live loads should be
limited to 18 ksi (125 MPa) when the radii of prestressing steel
curvature exceeds 29 ft (9 m), or to 10 ksi (70 MPa) when the
radii of prestressing-steel curvature does not exceed 12 ft
(3.6 m). A linear interpolation should be used for radii
between 12 and 29 ft (3.6 and 9 m) (AASHTO 2004). These
limits have been verified experimentally for prestressed
members with harped and straight strands strengthened with
externally bonded FRP (Rosenboom and Rizkalla 2006).
10.3.1.5 Creep-rupture and fatigue stress limits—To
avoid creep-rupture of the FRP reinforcement under
sustained stresses or failure due to cyclic stresses and fatigue
of the FRP reinforcement, the stress levels in the FRP
reinforcement under these stress conditions should not
exceed the limits provided in Section 10.2.9.
10.3.1.6 Nominal strength—The calculation procedure
to compute nominal strength should satisfy strain compatibility
and force equilibrium, and should consider the governing
mode of failure. The calculation procedure described herein
uses a trial-and-error method similar to that discussed in
Section 10.2.
For any assumed depth to the neutral axis, c, the effective
strain and stress in the FRP reinforcement can be computed
from Eq. (10-16) and (10-21), respectively. This equation
considers the governing mode of failure for the assumed
neutral axis depth. In Eq. (10-16), if the right side of the
equality controls, concrete crushing governs flexural failure
of the section. If εfd governs, then FRP rupture or debonding
governs the flexural failure of the section
ffe = Ef εfe
(10-21)
The strain level in the prestressed steel can be found from
Eq. (10-22) based on strain compatibility
2
Pe ⎛
e⎞
ε ps = ε pe + ----------⎜ 1 + ----2⎟ + ε pnet ≤ 0.035
Ac Ec ⎝
r ⎠
(10-22)
in which εpe is the effective strain in the prestressing steel
after losses, and εpnet is the net tensile strain in the
prestressing steel beyond decompression, at the nominal
strength. The value of εpnet will depend on the mode of
failure, and can be calculated using Eq. (10-23)
d p – c⎞
- for concrete crushing failure mode
ε pnet = 0.003 ⎛ -----------⎝ c ⎠
d p – c⎞
ε pnet = ( ε fe + ε bi ) ⎛ -----------⎝ df – c ⎠
(10-23a)
(10-23b)
for FRP rupture or debonding failure modes
The stress in the prestressing steel is calculated using the
material properties of the steel. For a typical seven-wire low-
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
relaxation prestressing strand, the stress-strain curve may be
approximated by the following equations (PCI 2004)
For Grade 250 ksi steel:
⎧ 28,500ε ps
for ε ps ≤ 0.0076
⎪
⎪
in in.-lb units
f ps = ⎨
0.04
⎪ 250 – ---------------------------- for ε ps > 0.0076
⎪
ε ps – 0.0064
⎩
(10-24a)
⎧ 196,500ε ps
for ε ps ≤ 0.0076
⎪
⎪
in SI units
f ps = ⎨
0.276
⎪ 1720 – ---------------------------- for ε ps > 0.0076
⎪
ε ps – 0.0064
⎩
⎧ 196,500ε ps
for ε ps ≤ 0.0086
⎪
⎪
f ps = ⎨
0.276 - for ε > 0.0086
⎪ 1860 – ------------------------ps
⎪
ε ps – 0.007
⎩
(10-27)
in which εpe is the effective prestressing strain, and εpnet,s is
the net tensile strain in the prestressing steel beyond
decompression at service. The value of εpnet,s depends on the
effective section properties at service, and can be calculated
using Eq. (10-28)
(10-24b)
in SI units
Ms e
ε pnet, s = --------- for uncracked section at service (10-28a)
Ec Ig
M snet e
for cracked section at service (10-28b)
ε pnet, s = --------------E c I cr
With the strain and stress level in the FRP and prestressing
steel determined for the assumed neutral axis depth, internal
force equilibrium may be checked using Eq. (10-25)
A p f ps + A f f fe
c = ---------------------------α 1 f c′ β 1 b
(10-26)
10.3.1.7 Stress in prestressing steel under service loads—
The stress level in the prestressing steel can be calculated
based on the actual condition (cracked or uncracked section)
of the strengthened reinforced concrete section. The strain in
prestressing steel at service, εps,s, can be calculated as
2
Pe ⎛
e⎞
ε ps, s = ε pe + ----------⎜ 1 + ----2⎟ + ε pnet, s
Ac Ec ⎝
r ⎠
For Grade 270 ksi steel:
⎧ 28,500ε ps
for ε ps ≤ 0.0086
⎪
⎪
in in.-lb units
f ps = ⎨
0.04 - for ε > 0.0086
⎪ 270 – ------------------------ps
⎪
ε ps – 0.007
⎩
β 1 c⎞
β 1 c⎞
M n = A p f ps⎛ d p – ------- + ψ f A f f fe ⎛ d f – ------⎝
⎝
2 ⎠
2 ⎠
440.2R-31
(10-25)
For the concrete crushing mode of failure, the equivalent
compressive stress block factor α1 can be taken as 0.85, and
β1 can be estimated per ACI 318-05. If FRP rupture, cover
delamination, or FRP debonding failure occurs, the use of
equivalent rectangular concrete stress block factors is
appropriate. Methods considering a nonlinear stress distribution
in the concrete can also be used.
The depth to the neutral axis, c, is found by simultaneously
satisfying Eq. (10-21) to (10-25), thus establishing internal
force equilibrium and strain compatibility. To solve for the
depth of the neutral axis, c, an iterative solution procedure
can be used. An initial value for c is first assumed, and the
strains and stresses are calculated using Eq. (10-21) to (10-24).
A revised value for the depth of neutral axis, c, is then
calculated from Eq. (10-25). The calculated and assumed
values for c are then compared. If they agree, then the proper
value of c is reached. If the calculated and assumed values do
not agree, another value for c is selected, and the process is
repeated until convergence is attained.
The nominal flexural strength of the section with FRP
external reinforcement can be computed using Eq. (10-26).
The additional reduction factor ψf = 0.85 is applied to the
flexural-strength contribution of the FRP reinforcement
where Msnet is the net service moment beyond decompression.
The stress in the prestressing steel under service loads can
then be computed from Eq. (10-24), and should be compared
against the limits described in Section 10.3.1.4.
10.3.1.8 Stress in FRP under service loads—Equation
(10-29) gives the stress level in the FRP reinforcement under
an applied moment within the elastic response range of the
member. The calculation procedure for the initial strain εbi at
the time of FRP installation will depend on the state of the
concrete section at the time of FRP installation and at service
condition. Prestressed sections can be uncracked at installation/
uncracked at service, uncracked at installation/cracked at
service, or cracked at installation/cracked at service. The initial
strain level on the bonded substrate, εbi, can be determined
from an elastic analysis of the existing member, considering
all loads that will be on the member during the installation of
the FRP system. The elastic analysis of the existing member
should be based on cracked or uncracked section properties,
depending of existing conditions. In most cases, the initial strain
before cracking is relatively small, and may conservatively
be ignored
E Ms yb
f f, s = ⎛ -----f ⎞ ----------- – ε bi E f
⎝ E c⎠ I
(10-29)
Depending on the actual condition at service (cracked or
uncracked section), the moment of inertia I can be taken as
the moment of inertia of the uncracked section transformed
to concrete, Itr , or the moment of inertia of the cracked
section transformed to concrete, Icr. The variable yb is the
440.2R-32
ACI COMMITTEE REPORT
distance from the centroidal axis of the gross section,
neglecting reinforcement, to the extreme bottom fiber. The
computed stress in the FRP under service loads should not
exceed the limits provided in Section 10.2.9.
CHAPTER 11—SHEAR STRENGTHENING
FRP systems have been shown to increase the shear
strength of existing concrete beams and columns by wrapping
or partially wrapping the members (Malvar et al. 1995;
Chajes et al. 1995; Norris et al. 1997; Kachlakev and
McCurry 2000). Orienting FRP fibers transverse to the axis
of the member or perpendicular to potential shear cracks is
effective in providing additional shear strength (Sato et al.
1996). Increasing the shear strength can also result in flexural
failures, which are relatively more ductile in nature
compared with shear failures.
11.1—General considerations
This chapter presents guidance on the calculation of added
shear strength resulting from the addition of FRP shear
reinforcement to a reinforced concrete beam or column. The
additional shear strength that can be provided by the FRP
system is based on many factors, including geometry of the
beam or column, wrapping scheme, and existing concrete
strength, but should always be limited in accordance with the
provisions of Chapter 9.
Shear strengthening using external FRP may be provided at
locations of expected plastic hinges or stress reversal and for
enhancing post-yield flexural behavior of members in
moment frames resisting seismic loads only by completely
wrapping the section. For external FRP reinforcement in the
form of discrete strips, the center-to-center spacing between
the strips should not exceed the sum of d/4 plus the width of
the strip.
11.2—Wrapping schemes
The three types of FRP wrapping schemes used to increase
the shear strength of prismatic, rectangular beams, or
columns are illustrated in Fig. 11.1. Completely wrapping
the FRP system around the section on all four sides is the
most efficient wrapping scheme and is most commonly used
in column applications where access to all four sides of the
column is usually available. In beam applications where an
integral slab makes it impractical to completely wrap the
member, the shear strength can be improved by wrapping the
FRP system around three sides of the member (U-wrap) or
bonding to two opposite sides of the member.
Although all three techniques have been shown to
improve the shear strength of a member, completely wrapping
the section is the most efficient, followed by the three-sided
U-wrap. Bonding to two sides of a beam is the least efficient
scheme.
In all wrapping schemes, the FRP system can be installed
continuously along the span of a member or placed as discrete
strips. As discussed in Section 9.3.3, the use of continuous
FRP reinforcement that completely encases a member and
potentially prevents migration of moisture is discouraged.
Fig. 11.1—Typical wrapping schemes for shear strengthening
using FRP laminates.
Table 11.1—Recommended additional reduction
factors for FRP shear reinforcement
ψf = 0.95
Completely wrapped members
ψf = 0.85
Three-side and two-opposite-sides schemes
11.3—Nominal shear strength
The design shear strength of a concrete member strengthened
with an FRP system should exceed the required shear
strength (Eq. (11-1)). The required shear strength of an FRPstrengthened concrete member should be computed with the
load factors required by ACI 318-05. The design shear
strength should be calculated by multiplying the nominal
shear strength by the strength reduction factor φ, as specified
by ACI 318-05
φVn ≥ Vu
(11-1)
The nominal shear strength of an FRP-strengthened
concrete member can be determined by adding the contribution
of the FRP external shear reinforcement to the contributions
from the reinforcing steel (stirrups, ties, or spirals) and the
concrete (Eq. (11-2)). An additional reduction factor ψf is
applied to the contribution of the FRP system
φVn = φ(Vc + Vs + ψfVf )
(11-2)
where Vc is calculated using Eq. (11-3) through Eq. (11-8) of
ACI 318-05, and Vs is calculated using Section 11.5.7.2 of
ACI 318-05. For prestressed members, Vc is the minimum of
Vci of Eq. (11-10) and Vcw of Eq. (11-12) of ACI 318-05. The
latter may also be computed based on Eq. (11-9) when
applicable (Reed et al. 2005).
Based on a reliability analysis using data from Bousselham
and Chaallal (2006), Deniaud and Cheng (2001, 2003),
Funakawa et al. (1997), Matthys and Triantafillou (2001),
and Pellegrino and Modena (2002), the reduction factor ψf of
0.85 is recommended for the three-sided FRP U-wrap or
two-opposite-sides strengthening schemes. Insufficient
experimental data exist to perform a reliability analysis for
fully-wrapped sections; however, there should be less
variability with this strengthening scheme as it is less bond
independent, and therefore, the reduction factor ψf of 0.95 is
recommended. The ψf factor was calibrated based on design
material properties. These recommendations are given in
Table 11.1.
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
440.2R-33
11.4—FRP contribution to shear strength
Figure 11.2 illustrates the dimensional variables used in
shear-strengthening calculations for FRP laminates. The
contribution of the FRP system to shear strength of a
member is based on the fiber orientation and an assumed
crack pattern (Khalifa et al. 1998). The shear strength
provided by the FRP reinforcement can be determined by
calculating the force resulting from the tensile stress in the
FRP across the assumed crack. The shear contribution of the
FRP shear reinforcement is then given by Eq. (11-3)
A fv f fe( sin α + cos α )d fv
V f = ------------------------------------------------------sf
(11-3)
Afv = 2ntf wf
(11-4)
where
The tensile stress in the FRP shear reinforcement at
nominal strength is directly proportional to the level of strain
that can be developed in the FRP shear reinforcement at
nominal strength
ffe = εfeEf
(11-5)
11.4.1 Effective strain in FRP laminates—The effective
strain is the maximum strain that can be achieved in the FRP
system at the nominal strength and is governed by the failure
mode of the FRP system and of the strengthened reinforced
concrete member. The licensed design professional should
consider all possible failure modes and use an effective
strain representative of the critical failure mode. The
following subsections provide guidance on determining this
effective strain for different configurations of FRP laminates
used for shear strengthening of reinforced concrete members.
11.4.1.1 Completely wrapped members—For reinforced
concrete column and beam members completely wrapped by
FRP, loss of aggregate interlock of the concrete has been
observed to occur at fiber strains less than the ultimate fiber
strain. To preclude this mode of failure, the maximum strain
used for design should be limited to 0.4% for members that
can be completely wrapped with FRP (Eq. (11-6a))
εfe = 0.004 ≤ 0.75εfu
(11-6a)
This strain limitation is based on testing (Priestley et al.
1996) and experience. Higher strains should not be used for
FRP shear-strengthening applications.
11.4.1.2 Bonded U-wraps or bonded face plies—FRP
systems that do not enclose the entire section (two- and
three-sided wraps) have been observed to delaminate from
the concrete before the loss of aggregate interlock of the
section. For this reason, bond stresses have been analyzed to
determine the usefulness of these systems and the effective
strain level that can be achieved (Triantafillou 1998a). The
effective strain is calculated using a bond-reduction coefficient
κv applicable to shear
εfe = κvεfu ≤ 0.004
(11-6b)
Fig. 11.2—Illustration of the dimensional variables used in
shear-strengthening calculations for repair, retrofit, or
strengthening using FRP laminates.
The bond-reduction coefficient is a function of the concrete
strength, the type of wrapping scheme used, and the stiffness of
the laminate. The bond-reduction coefficient can be computed
from Eq. (11-7) through (11-10) (Khalifa et al. 1998)
k1 k2 Le
κ v = --------------- ≤ 0.75 in in.-lb units
468ε fu
k1 k2 Le
κ v = ---------------------- ≤ 0.75 in SI units
11,900ε fu
(11-7)
The active bond length Le is the length over which the
majority of the bond stress is maintained. This length is
given by Eq. (11-8)
2500
L e = ------------------------ in in.-lb units
0.58
( n f t f E f)
23,300
L e = ------------------------- in SI units
0.58
( n f t f E f)
(11-8)
The bond-reduction coefficient also relies on two modification factors, k1 and k2, that account for the concrete strength and
the type of wrapping scheme used, respectively. Expressions for
these modification factors are given in Eq. (11-9) and (11-10)
f c′ ⎞ 2/3
k 1 = ⎛ ----------in in.-lb units
⎝ 4000⎠
f c′ ⎞
k 1 = ⎛ ----⎝ 27⎠
2/3
(11-9)
in SI units
⎧ d fv – L e
⎪ ------------------ for U-wraps
d fv
⎪
k2 = ⎨
⎪ d fv – 2L e
- for two sides bonded
⎪ -------------------⎩ d fv
(11-10)
440.2R-34
ACI COMMITTEE REPORT
The methodology for determining κv has been validated
for members in regions of high shear and low moment, such
as monotonically loaded simply supported beams. Although
the methodology has not been confirmed for shear strengthening
in areas subjected to combined high flexural and shear
stresses or in regions where the web is primarily in compression
(negative moment regions), it is suggested that κv is sufficiently
conservative for such cases. The design procedures outlined
herein have been developed by a combination of analytical
and empirical results (Khalifa et al. 1998).
Mechanical anchorages can be used at termination points to
develop larger tensile forces (Khalifa et al. 1999). The
effectiveness of such mechanical anchorages, along with the
level of tensile stress they can develop, should be substantiated
through representative physical testing. In no case, however,
should the effective strain in FRP laminates exceed 0.004.
11.4.2 Spacing—Spaced FRP strips used for shear
strengthening should be investigated to evaluate their
contribution to the shear strength. Spacing should adhere to
the limits prescribed by ACI 318-05 for internal steel shear
reinforcement. The spacing of FRP strips is defined as the
distance between the centerline of the strips.
11.4.3 Reinforcement limits—The total shear strength
provided by reinforcement should be taken as the sum of the
contribution of the FRP shear reinforcement and the steel
shear reinforcement. The sum of the shear strengths
provided by the shear reinforcement should be limited based
on the criteria given for steel alone in ACI 318-05, Section
11.5.6.9. This limit is stated in Eq. (11-11)
V s + V f ≤ 8 f c′ b w d
in in-lb units
V s + V f ≤ 0.66 f c′ b w d
(11-11)
in SI units
CHAPTER 12—STRENGTHENING OF MEMBERS
SUBJECTED TO AXIAL FORCE OR COMBINED
AXIAL AND BENDING FORCES
Confinement of reinforced concrete columns by means of
FRP jackets can be used to enhance their strength and
ductility. An increase in capacity is an immediate outcome
typically expressed in terms of improved peak load resistance.
Ductility enhancement, on the other hand, requires more
complex calculations to determine the ability of a member to
sustain rotation and drift without a substantial loss in
strength. This chapter applies only to members confined
with FRP systems.
12.1—Pure axial compression
FRP systems can be used to increase the axial compression
strength of a concrete member by providing confinement with
an FRP jacket (Nanni and Bradford 1995; Toutanji 1999).
Confining a concrete member is accomplished by orienting
the fibers transverse to the longitudinal axis of the member. In
this orientation, the transverse or hoop fibers are similar to
conventional spiral or tie reinforcing steel. Any contribution
of longitudinally aligned fibers to the axial compression
strength of a concrete member should be neglected.
Fig. 12.1—Schematic stress-strain behavior of unconfined
and confined RC columns (Rocca et al. 2006).
FRP jackets provide passive confinement to the compression
member, remaining unstressed until dilation and cracking of
the wrapped compression member occur. For this reason,
intimate contact between the FRP jacket and the concrete
member is critical.
Depending on the level of confinement, the uniaxial
stress-strain curve of a reinforced concrete column could be
depicted by one of the curves in Fig. 12.1, where fc′ and fcc′
represent the peak concrete strengths for unconfined and
confined cases, respectively. These strengths are calculated
as the peak load minus the contribution of the steel reinforcement, all divided by the cross-sectional area of the concrete.
The ultimate strain of the unconfined member corresponding
to 0.85fc′ (Curve (a)) is εcu. The strain εccu corresponds to:
a) 0.85fcc′ in the case of the lightly confined member (Curve (b));
and b) the failure strain in both the heavily confined-softening
case (the failure stress is larger than 0.85fcc′ —Curve (c)) or
in the heavily confined-hardening case (Curve (d)).
The definition of εccu at 0.85fcc′ or less is arbitrary,
although consistent with modeling of conventional concrete
(Hognestad 1951), and such that the descending branch of
the stress-strain curve at that level of stress (0.85fcc′ or
higher) is not as sensitive to the test procedure in terms of
rate of loading and stiffness of the equipment used.
The axial compressive strength of a nonslender, normalweight concrete member confined with an FRP jacket may
be calculated using the confined concrete strength (Eq. (12-1)).
The axial force acting on an FRP-strengthened concrete
member should be computed using the load factors required
by ACI 318-05, and the axial compression strength should be
calculated using the strength reduction factors φ for spiral
and tied members required by ACI 318-05.
For nonprestressed members with existing steel spiral
reinforcement
φPn = 0.85φ[0.85fcc′ (Ag – Ast) + fy Ast]
(12-1a)
For nonprestressed members with existing steel-tie
reinforcement
φPn = 0.8φ[0.85fcc′ (Ag – Ast) + fy Ast]
(12-1b)
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
440.2R-35
Several models that simulate the stress-strain behavior of
FRP-confined compression sections are available in the
literature (Teng et al. 2002; De Lorenzis and Tepfers 2003;
Lam and Teng 2003a). The stress-strain model by Lam and
Teng (2003a,b) for FRP-confined concrete has been adopted
by this committee and is illustrated in Fig. 12.2 and
computed using the following expressions
2
⎧
( Ec – E2 ) 2
⎪ E c ε c – ------------------------ε
c
fc = ⎨
4f c′
⎪
⎩ f c′ + E 2 ε c
0 ≤ ε c ≤ ε t′
(12-2a)
ε t′ ≤ ε c ≤ ε ccu
f cc′ – f c′
E 2 = -----------------ε ccu
(12-2b)
2f c′
ε t′ = ---------------Ec – E2
(12-2c)
The maximum confined concrete compressive strength fcc′
and the maximum confinement pressure fl are calculated
using Eq. (12-3) and (12-4), respectively (Lam and Teng
2003a,b) with the inclusion of an additional reduction factor
ψf = 0.95. The value of this reduction factor is based on the
committee’s judgment
Fig. 12.2—Lam and Teng’s stress-strain model for FRPconfined concrete (Lam and Teng 2003a).
branch in the stress-strain performance, as shown by Curve (d)
in Fig. 12.1. This limitation was later confirmed for circular
cross sections by Spoelstra and Monti (1999) using their
analytical model. A strain efficiency factor κε of 0.55 and a
minimum confinement ratio fl /fc′ of 0.08 (that is, ffuntf /(fc′ D)
≥ 0.073) should be used.
The maximum compressive strain in the FRP-confined
concrete εccu can be found using Eq. (12-6). This strain
should be limited to the value given in Eq. (12-7) to prevent
excessive cracking and the resulting loss of concrete integrity.
When this limit is applicable, the corresponding maximum
value of fcc′ should be recalculated from the stress-strain
curve (Concrete Society 2004).
fcc′ = fc′ = ψf 3.3κa fl
(12-3)
f ε 0.45
ε ccu = ε c′ ⎛ 1.50 + 12κ b ----l- ⎛ -----fe-⎞ ⎞
⎝
f c′ ⎝ ε c′ ⎠ ⎠
(12-6)
2E f nt f ε fe
f l = -------------------D
(12-4)
εccu ≤ 0.01
(12-7)
In Eq. (12-3), fc′ is the unconfined cylinder compressive
strength of concrete, and the efficiency factor κa accounts for
the geometry of the section, circular and noncircular, as
defined in Sections 12.1.1 and 12.1.2. In Eq. (12-4), the
effective strain level in the FRP at failure εfe is given by
εfe = κεεfu
(12-5)
The FRP strain efficiency factor κε accounts for the
premature failure of the FRP system (Pessiki et al. 2001),
possibly due to the multiaxial state of stress to which it is
subjected as opposed to the pure axial tension used for material
characterization. This behavior may also be related to stress
concentration regions caused by cracking of the concrete as
it dilates. Based on experimental calibration using mainly
CFRP-confined concrete specimens, an average value of
0.586 was computed for κε by Lam and Teng (2003a).
Similarly, a database of 251 test results (Harries and Carey
2003) computed a value of κε = 0.58 while experimental
tests on medium- and large-scale columns resulted in values
of κε = 0.57 and 0.61, respectively (Carey and Harries 2005).
Based on tests by Lam and Teng (2003a,b), the ratio fl /fc′
should not be less than 0.08. This is the minimum level of
confinement required to assure a nondescending second
In Eq. (12-6), the efficiency factor κb accounts for the
geometry of the section in the calculation of the ultimate
axial strain, as defined in Sections 12.1.1 and 12.1.2.
Strength enhancement for compression members with fc′
of 10,000 psi (70 MPa) or higher has not been experimentally
verified.
12.1.1 Circular cross sections—FRP jackets are most
effective at confining members with circular cross sections
(Demers and Neale 1999; Pessiki et al. 2001; Harries and
Carey 2003; Youssef 2003; Matthys et al. 2005; Rocca et al.
2006). The FRP system provides a circumferentially uniform
confining pressure to the radial expansion of the compression
member when the fibers are aligned transverse to the
longitudinal axis of the member. For circular cross sections,
the shape factors κa and κb in Eq. (12-3) and (12-6),
respectively, can be taken as 1.0.
12.1.2 Noncircular cross sections—Testing has shown
that confining square and rectangular members with FRP
jackets can provide marginal increases in the maximum axial
compressive strength fcc′ of the member (Pessiki et al. 2001;
Wang and Restrepo 2001; Harries and Carey 2003; Youssef
2003; Rocca et al. 2008). The provisions in this guide are not
recommended for members featuring side aspect ratios h/b
greater than 2.0, or face dimensions b or h exceeding 36 in.
(900 mm), unless testing demonstrates their effectiveness.
440.2R-36
ACI COMMITTEE REPORT
⎛ b---⎞ ( h – 2r ) + ⎛ h---⎞ ( b – 2r )
c
c
⎝ b⎠
⎝ h⎠
1 – ----------------------------------------------------------------------------- – ρ g
Ae
3A g
----- = ------------------------------------------------------------------------------------------------Ac
1 – ρg
2
Fig. 12.3—Equivalent circular cross section (Lam and Teng
2003b).
For noncircular cross sections, fl in Eq. (12-4) corresponds
to the maximum confining pressure of an equivalent circular
cross section with diameter D equal to the diagonal of the
rectangular cross section
D=
2
b +h
2
(12-8)
The shape factors κa in Eq. (12-3) and κb in Eq. (12-6)
depend on two parameters: the cross-sectional area of effectively confined concrete Ae, and the side-aspect ratio h/b, as
shown in Eq. (12-9) and (12-10), respectively
A b
κ a = -----e ⎛ ---⎞
A c ⎝ h⎠
2
A h 0.5
κ b = -----e ⎛ ---⎞
A c ⎝ b⎠
(12-9)
(12-10)
The generally accepted theoretical approach for the definition
of Ae consists of four parabolas within which the concrete is
fully confined, and outside of which negligible confinement
occurs (Fig. 12.3). The shape of the parabolas and the
resulting effective confinement area is a function of the
dimensions of the column (b and h), the radius of the corners
rc, and the longitudinal steel reinforcement ratio ρg, and can
be expressed as
2
(12-11)
12.1.3 Serviceability considerations—As loads approach
factored load levels, damage to the concrete in the form of
significant cracking in the radial direction might occur. The
FRP jacket contains the damage and maintains the structural
integrity of the column. At service load levels, however, this
type of damage should be avoided. In this way, the FRP
jacket will only act during overloading conditions that are
temporary in nature.
To ensure that radial cracking will not occur under service
loads, the transverse strain in the concrete should remain
below its cracking strain at service load levels. This corresponds to limiting the compressive stress in the concrete to
0.65fc′ . In addition, the service stress in the longitudinal steel
should remain below 0.60fy to avoid plastic deformation
under sustained or cyclic loads. By maintaining the specified
stress in the concrete at service, the stress in the FRP jacket
will be relatively low. The jacket is only stressed to significant
levels when the concrete is transversely strained above the
cracking strain and the transverse expansion becomes large.
Service load stresses in the FRP jacket should never exceed
the creep-rupture stress limit. In addition, axial deformations
under service loads should be investigated to evaluate their
effect on the performance of the structure.
12.2—Combined axial compression and bending
Wrapping with an FRP jacket can also provide strength
enhancement for a member subjected to combined axial
compression and flexure (Nosho 1996; Saadatmanesh et al.
1996; Chaallal and Shahawy 2000; Sheikh and Yau 2002;
Iacobucci et al. 2003; Bousias et al. 2004; Elnabelsy and
Saatcioglu 2004; Harajli and Rteil 2004; Sause et al. 2004;
Memon and Sheikh 2005).
For the purpose of predicting the effect of FRP confinement
on strength enhancement, Eq. (12-1) is applicable when the
eccentricity present in the member is less than or equal to
0.1h. When the eccentricity is larger than 0.1h, the methodology and equations presented in Section 12.1 can be used to
determine the concrete material properties of the member
cross section under compressive stress. Based on that, the P-M
diagram for the FRP-confined member can be constructed
using well-established procedures (Bank 2006).
The following limitations apply for members subjected to
combined axial compression and bending:
• The effective strain in the FRP jacket should be limited
to the value given in Eq. (12-12) to ensure the shear
integrity of the confined concrete
εfe = 0.004 ≤ κεεfu
•
(12-12)
The strength enhancement can only be considered
when the applied ultimate axial force and bending
moment, Pu and Mu, fall above the line connecting the
origin and the balanced point in the P-M diagram for
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Fig. 12.4—Representative interaction diagram.
the unconfined member (Fig. 12.4). This limitation
stems from the fact that strength enhancement is only
of significance for members in which compression
failure is the controlling mode (Bank 2006).
P-M diagrams may be developed by satisfying strain
compatibility and force equilibrium using the model for the
stress-strain behavior for FRP-confined concrete presented
in Eq. (12-2). For simplicity, the portion of the unconfined
and confined P-M diagrams corresponding to compressioncontrolled failure can be reduced to two bilinear curves
passing through three points (Fig 12.4). For values of
eccentricity greater than 0.1h and up to the point corresponding
to the balanced condition, the methodology provided in
Appendix A may be used for the computation of a simplified
interaction diagram. The values of the φ factors as established
in ACI 318-05 for both circular and noncircular cross
sections apply.
12.3—Ductility enhancement
Increased ductility of a section results from the ability to
develop greater compressive strains in the concrete before
compressive failure (Seible et al. 1997). The FRP jacket can
also serve to delay buckling of longitudinal steel reinforcement
in compression and to clamp lap splices of longitudinal steel
reinforcement.
For seismic applications, FRP jackets should be designed
to provide a confining stress sufficient to develop concrete
compression strains associated with the displacement
demands. The maximum compressive strain in concrete for
an FRP-confined member can be found by use of Eq. (12-6).
Shear forces should also be evaluated in accordance with
Chapter 11 to prevent brittle shear failure in accordance with
ACI 318-05.
12.3.1 Circular cross sections—The maximum compressive
strain for an FRP-confined members with circular cross
sections can be found from Eq. (12-6) with fcc′ from Eq. (12-3)
and using κb = 1.0.
12.3.2 Noncircular cross sections—The maximum
compressive strain for FRP-confined members with square
or rectangular sections can be found from Eq. (12-6), with
fcc′ from Eq. (12-3), and using κb as given in Eq. (12-10).
The confining effect of FRP jackets should be assumed to be
negligible for rectangular sections with aspect ratio h/b
exceeding 2.0, or face dimensions b or h exceeding 36 in.
(900 mm), unless testing demonstrates their effectiveness.
440.2R-37
12.4—Pure axial tension
FRP systems can be used to provide additional tensile
strength to a concrete member. Due to the linear-elastic
nature of FRP materials, the tensile contribution of the FRP
system is directly related to its strain level and is calculated
using Hooke’s Law.
The level of tension provided by the FRP is limited by the
design tensile strength of the FRP and the ability to transfer
stresses into the substrate through bond (Nanni et al. 1997).
The effective strain in the FRP can be determined based on
the criteria given for shear strengthening in Eq. (11-6)
through (11-9). The value of k1 in Eq. (11-7) can be taken as
1.0. A minimum bond length of 2Le (where Le is the active
bond length defined previously in Eq. (11-8)) should be
provided to develop this level of strain.
CHAPTER 13—FRP REINFORCEMENT DETAILS
This chapter offers guidance for detailing externally
bonded FRP reinforcement. Detailing will typically depend
on the geometry of the structure, the soundness and quality
of the substrate, and the levels of load that are to be sustained
by the FRP sheets or laminates. Many bond-related failures
can be avoided by following these general guidelines for
detailing FRP sheets or laminates:
• Do not turn inside corners such as at the intersection of
beams and joists with the underside of slabs;
• Provide a minimum 1/2 in. (13 mm) radius when the
sheet is wrapped around outside corners;
• Provide adequate development length; and
• Provide sufficient overlap when splicing FRP plies.
13.1—Bond and delamination
The actual distribution of bond stress in an FRP laminate
is complicated by cracking of the substrate concrete. The
general elastic distribution of interfacial shear stress and
normal stress along an FRP laminate bonded to uncracked
concrete is shown in Fig. 13.1.
For an FRP system installed according to Part 3 of this
guide, the weak link in the concrete/FRP interface is the
concrete. The soundness and tensile strength of the concrete
substrate will limit the overall effectiveness of the bonded
FRP system. Design requirements to mitigate FRP
debonding failure modes are discussed in Section 10.1.1.
13.1.1 FRP debonding—In reinforced concrete members
having relatively long shear spans or where the end peeling
(refer to Section 13.1.2) has been effectively mitigated,
debonding may initiate at flexural cracks, flexural/shear
cracks, or both, near the region of maximum moment. For
point-loading condition, the shear span is the distance from
a point load to the nearest support. Under loading, these
cracks open and induce high interfacial shear stress that
causes FRP debonding that propagates across the shear span
in the direction of decreasing moment. Typically, this failure
does not engage the aggregate in the concrete, progressing
through the thin mortar-rich layer comprising the surface of
the concrete beam. This failure mode is exacerbated in
regions having a high shear-moment ratio.
440.2R-38
ACI COMMITTEE REPORT
concrete cover layer from splitting. The area of the transverse clamping FRP U-wrap reinforcement Af,anchor can be
determined in accordance with Eq. (13-1) (Reed et al. 2005)
(A f f fu) longitudinal
A fanchor = --------------------------------------( E f κ v ε fu ) anchor
Fig. 13.1—Conceptual interfacial shear and normal stress
distributions along the length of a bonded FRP laminate
(Roberts and Haji-Kazemi 1989; Malek et al. 1998).
Fig. 13.2—Delamination caused by tension failure of the
concrete cover.
Mechanical anchorages can be effective in increasing
stress transfer (Khalifa et al. 1999), although their efficacy is
believed to result from their ability to resist the tensile
normal stresses rather than in enhancing the interfacial shear
capacity (Quattlebaum et al. 2005). Limited data suggest a
modest increase in FRP strain at debonding can be achieved
with the provision of transverse anchoring FRP wraps (Reed
et al. 2005). The performance of any anchorage system
should be substantiated through testing.
13.1.2 FRP end peeling—FRP end peeling (also referred
to as concrete cover delamination) can also result from the
normal stresses developed at the ends of externally bonded
FRP reinforcement. With this type of delamination, the
existing internal reinforcing steel essentially acts as a bond
breaker in a horizontal plane, and the concrete cover pulls
away from the rest of the beam (this may be exacerbated if
epoxy-coated steel reinforcement was used in the existing
member), as shown in Fig. 13.2.
The tensile concrete cover splitting failure mode is
controlled, in part, by the level of stress at the termination
point of the FRP. In general, the FRP end peeling failure
mode can be mitigated by using anchorage (transverse FRP
stirrups), by minimizing the stress at the FRP curtailment by
locating the curtailment as close to the region of zero
moment as possible, or by both. When the factored shear
force at the termination point is greater than 2/3 the concrete
shear strength (Vu > 0.67Vc), the FRP laminates should be
anchored with transverse reinforcement to prevent the
(13-1)
In which v is calculated using Eq. (11-7). Instead of
detailed analysis, the following general guidelines for the
location of cutoff points for the FRP laminate can be used to
avoid end peeling failure mode:
• For simply supported beams, a single-ply FRP laminate
should be terminated at least a distance equal to ldf past
the point along the span corresponding to the cracking
moment Mcr . For multiple-ply laminates, the termination
points of the plies should be tapered. The outermost ply
should be terminated not less than ldf past the point
along the span corresponding to the cracking moment.
Each successive ply should be terminated not less than
an additional 6 in. (150 mm) beyond the previous ply
(Fig. 13.3); and
• For continuous beams, a single-ply FRP laminate
should be terminated d/2 or 6 in. (150 mm) minimum
beyond the inflection point (point of zero moment
resulting from factored loads). For multiple-ply laminates,
the termination points of the plies should be tapered.
The outermost ply should be terminated no less than 6 in.
(150 mm) beyond the inflection point. Each successive
ply should be terminated no less than an additional 6 in.
(150 mm) beyond the previous ply. For example, if a
three-ply laminate is required, the ply directly in contact
with the concrete substrate should be terminated at least
18 in. (450 mm) past the inflection point (Fig. 13.3).
These guidelines apply for positive and negative
moment regions.
13.1.3 Development length—The bond capacity of FRP is
developed over a critical length ldf. To develop the effective
FRP stress at a section, the available anchorage length of FRP
should exceed the value given by Eq. (13-2) (Teng et al. 2001).
nE f t f
l df = 0.057 ----------f c′
l df =
nE f t f
----------f c′
in in.-lb units
(13-2)
in SI units
13.2—Detailing of laps and splices
Splices of FRP laminates should be provided only as
permitted on drawings, specifications, or as authorized by
the licensed design professional as recommended by the
system manufacturer.
The fibers of FRP systems should be continuous and
oriented in the direction of the largest tensile forces. Fiber
continuity can be maintained with a lap splice. For FRP
systems, a lap splice should be made by overlapping the
fibers along their length. The required overlap, or lap-splice
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
440.2R-39
Fig. 13.3—Graphical representation of the guidelines for allowable termination points of
a three-ply FRP laminate.
length, depends on the tensile strength and thickness of the
FRP material system and on the bond strength between adjacent
layers of FRP laminates. Sufficient overlap should be
provided to promote the failure of the FRP laminate before
debonding of the overlapped FRP laminates. The required
overlap for an FRP system should be provided by the material
manufacturer and substantiated through testing that is
independent of the manufacturer.
Jacket-type FRP systems used for column members should
provide appropriate development area at splices, joints, and
termination points to ensure failure through the FRP jacket
thickness rather than failure of the spliced sections.
For unidirectional FRP laminates, lap splices are required
only in the direction of the fibers. Lap splices are not required
in the direction transverse to the fibers. FRP laminates
consisting of multiple unidirectional sheets oriented in more
than one direction or multidirectional fabrics require lap
splices in more than one direction to maintain the continuity
of the fibers and the overall strength of the FRP laminates.
13.3—Bond of near-surface-mounted systems
For NSM systems, the minimum dimension of the grooves
should be taken at least 1.5 times the diameter of the FRP bar
(De Lorenzis and Nanni 2001b; Hassan and Rizkalla 2003).
When a rectangular bar with large aspect ratio is used,
however, the limit may lose significance due to constructibility. In such a case, a minimum groove size of 3.0ab ×
1.5bb, as depicted in Fig. 13.4, is suggested, where ab is the
smallest bar dimension. The minimum clear groove spacing
for NSM FRP bars should be greater than twice the depth of
the NSM groove to avoid overlapping of the tensile stresses
around the NSM bars. Furthermore, a clear edge distance of
Fig. 13.4—Minimum dimensions of grooves.
four times the depth of the NSM groove should be provided
to minimize the edge effects that could accelerate debonding
failure (Hassan and Rizkalla 2003).
Bond properties of the NSM FRP bars depend on many
factors such as cross-sectional shape and dimensions and
surface properties of the FRP bar (Hassan and Rizkalla 2003;
De Lorenzis et al. 2004). Figure 13.5 shows the equilibrium
condition of an FRP bar with an embedded length equal to its
development length ldb having a bond strength of τmax.
Using a triangular stress distribution, the average bond
strength can be expressed as τb = 0.5τmax. Average bond
strength τb for NSM FRP bars in the range of 500 to 3000 psi
(3.5 to 20.7 MPa) has been reported (Hassan and Rizkalla
2003; De Lorenzis et al. 2004); therefore, τb = 1000 psi (6.9
MPa) is recommended for calculating the bar development
length. Via force equilibrium, the following equations for
development length can be derived
db
l db = ------------ f for circular bars
4 ( τ b ) fd
(13-3)
440.2R-40
ACI COMMITTEE REPORT
•
•
•
•
•
•
Fig. 13.5—Transfer of force in NSM FRP bars.
ab bb
l db = ---------------------------------- f for rectangular bars
2 ( a b + b b ) ( τ b ) fd
(13-4)
CHAPTER 14—DRAWINGS, SPECIFICATIONS,
AND SUBMITTALS
14.1—Engineering requirements
Although federal, state, and local codes for the design of
externally bonded FRP systems do not exist, other applicable
code requirements may influence the selection, design, and
installation of the FRP system. For example, code requirements
related to fire or potable water may influence the selection of
the coatings used with the FRP system. All design work
should be performed under the guidance of a licensed design
professional familiar with the properties and applications of
FRP strengthening systems.
14.2—Drawings and specifications
The licensed design professional should document calculations summarizing the assumptions and parameters used to
design the FRP strengthening system and should prepare
design drawings and project specifications. The drawings
and specifications should show, at a minimum, the following
information specific to externally applied FRP systems:
• FRP system to be used;
• Location of the FRP system relative to the existing
structure;
• Dimensions and orientation of each ply, laminate, or
NSM bar;
• Number of plies and bars and the sequence of installation;
• Location of splices and lap length;
• General notes listing design loads and allowable strains
in the FRP laminates;
• Material properties of the FRP laminates and concrete
substrate;
• Concrete surface preparation requirements, including
corner preparation, groove dimensions for NSM bars,
and maximum irregularity limitations;
Installation procedures, including surface temperature
and moisture limitations, and application time limits
between successive plies;
Curing procedures for FRP systems;
Protective coatings and sealants, if required;
Shipping, storage, handling, and shelf-life guidelines;
Quality control and inspection procedures, including
acceptance criteria; and
In-place load testing of installed FRP system, if necessary.
14.3—Submittals
Specifications should require the FRP system manufacturer,
installation contractor, inspection agency (if required), and
all those involved with the project to submit product information and evidence of their qualifications and experience to
the licensed design professional for review.
14.3.1 FRP system manufacturer—Submittals required of
the FRP system manufacturer should include:
• Product data sheets indicating the physical, mechanical,
and chemical characteristics of the FRP system and all
its constituent materials;
• Tensile properties of the FRP system, including the
method of reporting properties (net fiber or gross
laminate), test methods used, and the statistical basis
used for determining the properties (Section 4.3);
• Installation instructions, maintenance instructions, and
general recommendations regarding each material to be
used. Installation procedures should include surface
preparation requirements;
• Manufacturer’s MSDS for all materials to be used;
• QC procedure for tracking FRP materials and material
certifications;
• Durability test data for the FRP system in the types of
environments expected;
• Structural test reports pertinent to the proposed
application; and
• Reference projects.
14.3.2 FRP system installation contractor—Submittals
required of the FRP system installation contractor should
include:
• Documentation from the FRP system manufacturer of
having been trained to install the proposed FRP system;
• Project references, including installations similar to the
proposed installation. For example, for an overhead
application, the contractor should submit a list of
previous installations involving the installation of the
proposed FRP system in an overhead application;
• Evidence of competency in surface preparation techniques;
• QC testing procedures including voids and delaminations,
FRP bond to concrete, and FRP tensile properties; and
• Daily log or inspection forms used by the contractor.
14.3.3 FRP system inspection agency—If an independent
inspection agency is used, submittals required of that agency
should include:
• A list of inspectors to be used on the project and their
qualifications;
• Sample inspection forms; and
• A list of previous projects inspected by the inspector.
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
440.2R-41
PART 5—DESIGN EXAMPLES
CHAPTER 15—DESIGN EXAMPLES
15.1—Calculation of FRP system tensile properties
This example illustrates the derivation of material properties based on net-fiber area versus the properties based on grosslaminate area. As described in Section 4.3.1, both methods of determining material properties are valid. It is important, however,
that any design calculations consistently use material properties based on only one of the two methods (for example, if the grosslaminate thickness is used in any calculation, the strength based on gross-laminate area should be used in the calculations as
well). Reported design properties should be based on a population of 20 or more coupons tested in accordance with ASTM
D3039. Reported properties should be statistically adjusted by subtracting three standard deviations from the mean tensile stress
and strain, as discussed in Section 4.3.1.
A test panel is fabricated from two plies of a carbon fiber/resin unidirectional FRP system using the wet layup technique.
Based on the known fiber content of this FRP system, the net-fiber area is 0.0065 in.2/in. (0.165 mm2/mm) width per ply.
After the system has cured, five 2 in. (50.8 mm) wide test coupons are cut from the panel. The test coupons are tested in tension
to failure in accordance with ASTM D3039. Tabulated in Table 15.1 are the results of the tension tests.
Table 15.1—FRP system tension test results
Specimen width
Measured coupon thickness
Measured rupture load
Coupon ID
T-1
in.
2
mm
50.8
in.
0.055
mm
1.40
kips
17.8
kN
79.2
T-2
T-3
2
2
50.8
50.8
0.062
0.069
1.58
1.75
16.4
16.7
72.9
74.3
T-4
T-5
2
2
50.8
50.8
0.053
0.061
1.35
1.55
16.7
17.4
74.3
77.4
Average
2
50.8
0.060
1.52
17.0
75.6
Net-fiber area property calculations
Calculate Af using the
known, net-fiber area ply
thickness:
Gross-laminate area property calculations
Af = (2)(0.0065 in.2/in.)(2 in.) = 0.026 in.2
Calculate Af using the
average, measured laminate
thickness:
Af = (0.060 in.)(2 in.) = 0.120 in.2
Af = ntf wf
Af = (2)(0.165 mm2/mm)(50.8 mm) = 16.8 mm2
Af = tf wf
Af = (1.52 mm)(50.8 mm) = 77.4 mm2
Calculate the average FRP
system tensile strength
based on net-fiber area:
17 kips
f fu = -----------------------2 = 650 ksi
0.026 in.
Calculate the average FRP
system tensile strength based
on gross-laminate area:
17 kips
f fu = -----------------------2 = 140 ksi
0.120 in.
Average rupture load
f fu = --------------------------------------------------Af
Calculate the average FRP
system tensile strength per
unit width based on netfiber area:
2
75.62 kN
f fu = -----------------------2 = 4.5 kN/mm
16.8 mm
2
(650 ksi)(0.026 in. )
p fu = ------------------------------------------------- = 8.4 kips/in.
2 in.
2
f fu A f
p fu = --------wf
Average rupture load
f fu = --------------------------------------------------Af
Calculate the average FRP
system tensile strength per
unit width based on laminate
area:
2
( 4.5 kN/mm ) ( 16.8 mm -)
p fu = --------------------------------------------------------------= 1.49 kN/mm
50.8 mm
2
75.62 kN
f fu = -----------------------2 = 0.997 kN/mm
77.4 mm
2
(140 ksi)(0.120 in. )
p fu = ------------------------------------------------- = 8.4 kips/in.
2 in.
2
f fu A f
p fu = --------wf
2
0.98kN/mm ) ( 77.4 mm -)
p fu = (---------------------------------------------------------------= 1.49 kN/mm
50.8 mm
440.2R-42
ACI COMMITTEE REPORT
15.2—Comparison of FRP systems’ tensile properties
Two FRP systems are being considered for strengthening concrete members. The mechanical properties of two FRP systems
are available from respective manufacturers. System A consists of dry, carbon-fiber unidirectional sheets and is installed with
an adhesive resin using the wet layup technique. System B consists of precured carbon fiber/resin laminates that are bonded to
the concrete surface with an adhesive resin. Excerpts from the data sheets provided by the FRP system manufacturers are given
in Table 15.2. After reviewing the material data sheets sent by the FRP system manufacturers, the licensed design professional
compares the tensile strengths of the two systems.
Table 15.2—Material properties and description of two types of FRP systems
System A
(excerpts from data sheet)
System type: dry, unidirectional sheet
System B
(excerpts from data sheet)
System type: precured, unidirectional laminate
Fiber type: high-strength carbon
Polymer resin: epoxy
Fiber type: high-strength carbon
Polymer resin: epoxy
System A is installed using a wet layup procedure where the dry carbon-fiber System B’s precured laminates are bonded to the concrete substrate using
sheets are impregnated and adhered with an epoxy resin on-site.
System B’s epoxy paste adhesive.
Mechanical properties*†‡
Mechanical properties*†
tf = 0.013 in. (0.33 mm)
ffu*
tf = 0.050 in. (1.27 mm)
ffu*
2
= 550 ksi (3792 N/mm )
= 380 ksi (2620 N/mm2)
εfu* = 1.6%
εfu* = 1.5%
Ef = 33,000 ksi (227,527 N/mm2)
Ef = 22,000 ksi (151,724 N/mm2)
Notes on System B:
Notes on System A:
*
Reported properties are based on a population of 20 or more coupons tested in accordance *Reported properties are based on a population of 20 or more coupons tested in accordance
with ASTM D3039.
with ASTM D3039.
†
Reported properties have been statistically adjusted by subtracting three standard deviations †Reported properties have been statistically adjusted by subtracting three standard deviations
from the mean tensile stress and strain.
from the mean tensile stress and strain.
‡
Thickness is based on the net-fiber area for one ply of the FRP system. Resin is excluded.
Actual installed thickness of cured FRP is 0.04 to 0.07 in. (1.0 to 1.8 mm) per ply.
Because the data sheets for both systems are reporting statistically based properties, it is possible to directly compare the
tensile strength and modulus of both systems.
Procedure
Step 1A—Calculate the tensile strength per unit
width of System A
*
pfu
Calculation in SI units
*
pfu
= (550 ksi)(0.013 in.) = 7.15 kips/in.
*
pfu
= (3.79 kN/mm2)(0.33 mm) = 1.25 kN/mm
*
pfu
= (380 ksi)(0.050 in.) = 19 kips/in.
*
pfu
= (2.62 kN/mm2)(1.27 mm) = 3.33 kN/mm
kf = (33,000 ksi)(0.013 in.) = 429 kips/in.
kf = (227.5 kN/mm2)(0.33 mm) = 75.1 kN/mm
kf = (22,000 ksi)(0.050 in.) = 1100 kips/in.
kf = (151.7 kN/mm2)(1.27 mm) = 192.7 kN/mm
p fu* (System B)
19 kips/in. = 2.66
--------------------------------- = -------------------------p fu* (System A)
7.5 kips/in.
p fu* (System B)
3.33 kN/mm = 2.66
--------------------------------- = ------------------------------p fu* (System A)
75.1 kN/mm
= ffu* tf
Step 1B—Calculate the tensile strength per unit
width of System B
*
pfu
Calculation in inch-pound units
= ffu* tf
Step 2A—Calculate the tensile modulus per unit
width of System A
kf = Ef tf
Step 2B—Calculate the tensile modulus per unit
width of System B
kf = Ef tf
Step 3—Compare the two systems
Compare the tensile strengths:
*
(System A)
pfu
*
(System B)
pfu
Compare the stiffnesses:
kf (System A)
kf (System B)
∴ three plies of System A are required for each ply ∴ three plies of System A are required for each ply
of System B for an equivalent tensile strength
of System B for an equivalent tensile strength
k f (System B) 1100 kips/in.
------------------------------= ------------------------------- = 2.56
k f (System A)
429 kips/in.
k f (System A)
192.7 kN/mm = 2.56
------------------------------= ---------------------------------k f (System B)
75.1 kN/mm
∴ three plies of System A are required for each ply ∴ three plies of System A are required for each ply
of System B for an equivalent stiffness
of System B for an equivalent stiffness
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
440.2R-43
Because all the design procedures outlined in this document limit the strain in the FRP material, the full nominal strength of
the material is not used and should not be the basis of comparison between two material systems. When considering various
FRP material systems for a particular application, the FRP systems should be compared based on equivalent stiffness only. In
addition, each FRP system under consideration should have the ability to develop the strain level associated with the effective
strain level required by the application without rupturing, εfu > εfe.
In many instances, it may be possible to vary the width of the FRP strip as opposed to the number of plies (use larger widths for
systems with lower thicknesses and vice versa). In such instances, equivalent stiffness calculations typically will not yield
equivalent contributions to the strength of a member. In general, thinner (lower ntf) and wider (higher wf) FRP systems will provide
a higher level of strength to a member due to lower bond stresses. The exact equivalency, however, can only be found by
performing complete calculations (according to procedures described in Chapters 10, 11, and 12 of this guide) for each system.
15.3—Flexural strengthening of an interior reinforced concrete beam with FRP laminates
A simply supported concrete beam reinforced with three No. 9 bars (Fig. 15.1) is located in an unoccupied warehouse and is
subjected to a 50% increase in its live-load-carrying requirements. An analysis of the existing beam indicates that the beam still
has sufficient shear strength to resist the new required shear strength and meets the deflection and crack-control serviceability
requirements. Its flexural strength, however, is inadequate to carry the increased live load.
Length of the beam l
Width of the beam w
24 ft
12 in.
7.32 m
305 mm
d
h
21.5 in.
24 in.
546 mm
609.6 mm
fc′
5000 psi
34.5 N/mm2
fy
60 ksi
φMn without FRP
266 k-ft
414 N/mm2
361 kN-m
Bars
No. 9
φ= 28.6 mm
Fig. 15.1—Schematic of the idealized simply supported
beam with FRP external reinforcement.
Summarized in Table 15.3 are the existing and new loadings and associated midspan moments for the beam.
Table 15.3—Loadings and corresponding moments
Loading/moment
Dead loads wDL
Existing loads
Anticipated loads
1.00 k/ft
14.6 N/mm
1.00 k/ft
14.6 N/mm
Live load wLL
1.20 k/ft
17.5 N/mm
1.80 k/ft
26.3 N/mm
Unfactored loads (wDL + wLL )
2.20 k/ft
32.1 N/mm
2.80 k/ft
40.9 N/mm
Unstrengthened load limit (1.1wDL + 0.75wLL )
N/A
N/A
2.50 k/ft
35.8 N/mm
Factored loads (1.2wDL + 1.6wLL )
3.12 k/ft
45.5 N/mm
4.08 k/ft
59.6 N/mm
Dead-load moment MDL
72 k-ft
98 kN-m
72 k-ft
98 kN-m
Live-load moment MLL
86 k-ft
117 kN-m
130 k-ft
176 kN-m
Service-load moment Ms
158 k-ft
214 kN-m
202 k-ft
274 kN-m
Unstrengthened moment limit (1.1MDL + 0.75MLL )
N/A
N/A
177 k-ft
240 kN-m
Factored moment Mu
224 k-ft
304 kN-m
294.4 k-ft
399 kN-m
The existing reinforced concrete beam should be strengthened with the FRP system described in Table 15.4, specifically, two
12 in. (305 mm) wide x 23.0 ft (7 m) long plies bonded to the soffit of the beam using the wet layup technique.
Table 15.4—Manufacturer’s reported FRP system properties
Thickness per ply tf
0.040 in.
1.02 mm
Ultimate tensile strength ffu*
90 ksi
621 N/mm2
0.015 in./in.
0.015 mm/mm
5360 ksi
37,000 N/mm2
Rupture strain εfu*
Modulus of elasticity of FRP laminates Ef
440.2R-44
ACI COMMITTEE REPORT
By inspection, the level of strengthening is reasonable in that it does meet the strengthening limit criteria specified in Eq. (9-1). That
is, the existing moment strength without FRP, (φMn)w/o = 266 k-ft (361 kN-m), is greater than the unstrengthened moment limit,
(1.1MDL + 0.75MLL)new = 177 k-ft (240 kN-m). The design calculations used to verify this configuration follow.
Procedure
Calculation in inch-pound units
Calculation in SI metric units
ffu = (0.95)(90 ksi) = 85 ksi
εfu = (0.95)(0.015 in./in.) = 0.0142 in./in.
ffu = (0.95)(621 N/mm2) = 590 N/mm2
εfu = (0.95)(0.015 mm/mm) = 0.0142 mm/mm
β1 from ACI 318-05, Section 10.2.7.3
f c′
β1 = 1.05 – 0.05 ----------- = 0.80
1000
f c′
β1 = 1.05 – 0.05 ------ = 0.80
6.9
Ec = 57,000√fc′
E c = 57,000 5000 psi = 4,030,000 psi
E c = 4700 34.5 N/mm = 27,600 N/mm2
As = 3(1.00 in.2) = 3.00 in.2
As = 3(645 mm2) = 1935 mm2
Af = (2 plies)(0.040 in./ply)(12 in.) = 0.96 in.2
Af = (2 plies)(1.02 mm/ply)(305 mm) = 619 mm2
( 864 k-in. ) [ 24 in. – ( 0.334 ) ( 21.5 in. ) ]
ε bi = --------------------------------------------------------------------------------------------4
( 5937 in. ) ( 4030 ksi )
( 97.6 kN-mm ) [ 609.6 mm – ( 0.334 ) ( 546.1 mm ) -]
εbi = ---------------------------------------------------------------------------------------------------------------------6
4
2
( 2471 × 10 mm ) ( 27.6 kN/mm )
εbi = 0.00061
εbi = 0.00061
5000 psi
ε fd = 0.083 ---------------------------------------------------------------2 ( 5,360,000 psi ) ( 0.04 in. )
34.5 N/mm
ε fd = 0.41 --------------------------------------------------------------------2
2 ( 37,000 N/mm ) ( 1.02 mm )
= 0.009 ≤ 0.9(0.0142) = 0.0128
= 0.009 ≤ 0.9(0.0142) = 0.0128
c = (0.20)(21.5 in.) = 4.30 in.
c = (0.20)(546.1 mm) = 109 mm
Step 1—Calculate the FRP system design
material properties
The beam is located in an interior space and
a CFRP material will be used. Therefore,
per Table 9.1, an environmental reduction
factor of 0.95 is suggested.
ffu = CE ffu*
εfu = CEεfu*
Step 2—Preliminary calculations
Properties of the concrete:
2
Properties of the existing reinforcing steel:
Properties of the externally bonded FRP
reinforcement:
Af = ntf wf
Step 3—Determine the existing state of
strain on the soffit
The existing state of strain is calculated
assuming the beam is cracked and the only
loads acting on the beam at the time of the FRP
installation are dead loads. A cracked section
analysis of the existing beam gives k = 0.334
and Icr = 5937 in.4 = 2471 × 106 mm4
M DL ( d f – kd )
ε bi = ------------------------------I cr E c
Step 4—Determine the design strain of the
FRP system
The design strain of FRP accounting for
debonding failure mode εfd is calculated
using Eq. (10-2)
2
Because the design strain is smaller than the
rupture strain, debonding controls the
design of the FRP system.
Step 5—Estimate c, the depth to the
neutral axis
A reasonable initial estimate of c is 0.20d.
The value of the c is adjusted after checking
equilibrium.
c = 0.20d
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Procedure
440.2R-45
Calculation in inch-pound units
Calculation in SI metric units
d f – c⎞
– εbi ≤ εfd
εfe = 0.003 ⎛ -----------⎝ c ⎠
in. – 4.3 in.
εfe = 0.003 ⎛ 24
----------------------------------⎞ – 0.00061 ≤ 0.009
⎝
⎠
4.3 in.
609.6 mm – 109.2 mm
εfe = 0.003 ⎛ ------------------------------------------------------⎞ – 0.00061 ≤ 0.009
⎝
⎠
109.2 mm
Note that for the neutral axis depth selected,
FRP debonding would be in the failure
mode because the second expression in this
equation controls. If the first expression
governed, then concrete crushing would be
in the failure mode.
εfe = 0.0131 > 0.009
εfe = 0.0131 > 0.009
εfe = εfd = 0.009
εfe = εfd = 0.009
4.3 in.
⎞ = 0.0021
εc = (0.009 + 0.00061) ⎛ ---------------------------------⎝ 24 in. – 4.3 in.⎠
109.2 mm
εc = (0.009 + 0.00061) ⎛ -----------------------------------------------------⎞ = 0.0021
⎝ 609.6 mm – 109.2 mm⎠
in. – 4.3 in.-⎞ = 0.0084
εs = (0.009 + 0.00061) ⎛ 21.5
-------------------------------------⎝ 24 in. – 4.3 in. ⎠
mm – 109.2 mm-⎞ = 0.0084
εs = (0.009 + 0.00061) ⎛ 546.1
----------------------------------------------------⎝ 609.6 mm – 109.2 mm⎠
fs = Esεs ≤ fy
fs = (29,000 ksi)(0.0084) ≤ 60 ksi
fs = 244 ksi ≤ 60 ksi
Hence, fs = 60 ksi
fs = (200 kN/mm2)(0.0084) ≤ 0.414 kN/mm2
fs = 1.68 kN/mm2 ≤ 0.414 kN/mm2
Hence, fs = 0.414 kN/mm2
ffe = Ef εfe
ffe = (5360 ksi)(0.009) = 48.2 ksi
ffe = (37 kN/mm2)(0.009) = 0.33 kN/mm2
Step 9—Calculate the internal force
resultants and check equilibrium
Concrete stress block factors may be calculated using ACI 318-05. Approximate stress
block factors may also be calculated based
on the parabolic stress-strain relationship for
concrete as follows:
1.7 ( 5000 )
ε c′ = -------------------------6 = 0.0021
4030 × 10
( 34.5 )- = 0.0021
ε c′ = 1.7
---------------------27,600
4ε′c – ε c
β 1 = ----------------------6ε′c – 2ε c
4 ( 0.0021 ) – 0.0021
β 1 = ------------------------------------------------------- = 0.749
6 ( 0.0021 ) – 2 ( 0.0021 )
4 ( 0.0021 ) – 0.0021
β 1 = ------------------------------------------------------- = 0.749
6 ( 0.0021 ) – 2 ( 0.0021 )
Step 6—Determine the effective level of
strain in the FRP reinforcement
The effective strain level in the FRP may be
found from Eq. (10-3).
Because FRP controls the failure of the
section, the concrete strain at failure εc may
be less than 0.003 and can be calculated
using similar triangles:
c ⎞
εc = (εfe + εbi) ⎛ -----------⎝ d f – c⎠
Step 7—Calculate the strain in the existing
reinforcing steel
The strain in the reinforcing steel can be
calculated using similar triangles according to
Eq. (10-10).
d–c
εs = (εfe + εbi)⎛ ------------⎞
⎝ d f – c⎠
Step 8—Calculate the stress level in the
reinforcing steel and FRP
The stresses are calculated using Eq. (10-11)
and (10-9).
2
3ε′c ε c – ε c
α 1 = -----------------------2
3β 1 ε c′
2
3 ( 0.0021 ) ( 0.0021 ) – ( 0.0021 )
α 1 = --------------------------------------------------------------------------- = 0.886
2
3 ( 0.749 ) ( 0.0021 )
2
3 ( 0.0021 ) ( 0.0021 ) – ( 0.0021 )
α 1 = --------------------------------------------------------------------------- = 0.886
2
3 ( 0.749 ) ( 0.0021 )
where εc′ is strain corresponding to fc′
calculated as
1.7f c′
ε c′ = -----------Ec
Force equilibrium is verified by checking the
initial estimate of c with Eq. (10-12).
A s f s + A f f fe
c = ------------------------α 1 f c′ β 1 b
2
c=
2
( 3.00 in. ) ( 60 ksi ) + ( 0.96 in. ) ( 48.2 ksi )
c = ---------------------------------------------------------------------------------------------------( 0.886 ) ( 5 ksi ) ( 0.749 ) ( 12 in. )
c = 5.68 in. ≠ 4.30 in. n.g.
∴ Revise estimate of c and repeat Steps 6 through 9
until equilibrium is achieved.
2
2
2
2
(1935.48 mm ) ( 414 N/mm ) + ( 619 mm ) ( 330 N/mm )
---------------------------------------------------------------------------------------------------------------------------------------2
( 0.886 ) ( 34.5 N/mm ) ( 0.749 ) ( 304.8 mm )
c = 149 mm ≠ 109 in. n.g.
∴ Revise estimate of c and repeat Steps 6 through 9
until equilibrium is achieved.
440.2R-46
ACI COMMITTEE REPORT
Procedure
Calculation in inch-pound units
Step 10—Adjust c until force equilibrium
is satisfied
Steps 6 through 9 were repeated several
times with different values of c until equilibrium was achieved. The results of the final
iteration are
( 3.00 in. ) ( 60 ksi ) + ( 0.96 in. ) ( 48.2 ksi )
c = ---------------------------------------------------------------------------------------------------( 0.928 ) ( 5 ksi ) ( 0.786 ) ( 12 in. )
c = -----------------------------------------------------------------------------------------------------------------------------------------
c = 5.17 in. ✓ OK
c = 131 mm ✓ OK
∴ the value of c selected for the final iteration is correct.
∴ the value of c selected for the final iteration is correct.
2
( 5.17 in. -)⎞
M ns = ( 3.00 in. ) ( 60 ksi ) ⎛ 21.5 in. – 0.786
-----------------------------------⎝
⎠
2
M ns = ( 1935.5 mm ) ( 414 N/mm )
Mns = 3504 k-in. = 292 k-ft
Mns = 3.963 × 108 N-mm = 396.3 kN-m
c = 5.17 in.; εs = 0.0083; fs = fy = 60 ksi;
β1 = 0.786; α1 = 0.928; and ffd = 48.2 ksi
2
2
Calculation in SI metric units
2
2
2
2
(1935.5 mm ) ( 414 N/mm ) + ( 619 mm ) ( 330 N/mm )
2
( 0.928 ) ( 34.5 N/mm ) ( 0.786 ) ( 304.8 mm )
Step 11—Calculate flexural strength
components
The design flexural strength is calculated
using Eq. (10-13). An additional reduction
factor, ψf = 0.85, is applied to the contribution of the FRP system.
Steel contribution to bending:
β 1 c⎞
M ns = A s f s ⎛ d – ------⎝
2 ⎠
2
2
0.786 ( 131 mm )⎞
⎛ 546.1 mm – ------------------------------------⎝
⎠
2
FRP contribution to bending:
β 1 c⎞
M nf = A f f fe ⎛ d f – ------⎝
2 ⎠
( 131 mm )
2
( 5.17 in. )-⎞ M = ( 619 mm 2 ) ( 330 N/mm 2 ) ⎛ 609.6 mm – 0.786
--------------------------------------⎞⎠
M nf = ( 0.96 in. ) ( 48.2 ksi ) ⎛ 24 in. – 0.786
-----------------------------------nf
⎝
2
⎝
⎠
2
Mnf = 1020 k-in. = 85 k-ft
Mnf = 1.140 × 108 N-mm = 114 kN-m
φMn = 0.9[292 k-ft + 0.85(85 k-ft)]
φMn = 327 k-ft ≥ Mu = 294 k-ft
φMn = 0.9[396.3 kN-m + 0.85(114 kN-m)]
φMn = 443 kN-m ≥ Mu = 399 kN-m
∴ the strengthened section is capable of sustaining
the new required moment strength.
∴ the strengthened section is capable of sustaining
the new required moment strength.
Step 12—Calculate design flexural
strength of the section
The design flexural strength is calculated
using Eq. (10-1) and (10-13). Because εs =
0.0083 > 0.005, a strength reduction factor
of φ = 0.90 is appropriate per Eq. (10-5).
φMn = φ[Mns + ψf Mnf ]
Step 13—Check service stresses in the
reinforcing steel and the FRP
Calculate the elastic depth to the cracked
neutral axis. This can be simplified for a
rectangular beam without compression
reinforcement as follows:
k =
Es
E 2
E
E d
⎛ ρ ---+ ρ f -----f ⎞ + 2 ⎛ ρ s -----s + ρ f -----f ⎛ ----f⎞ ⎞
⎝ s E-c
⎝ Ec
E c⎠
Ec ⎝ d ⎠ ⎠
*
E
E
– ⎛ ρ s -----s + ρ f -----f ⎞
⎝ Ec
E c⎠
See EQUATION NOTE I (U.S.) after Step 14.
**
See EQUATION NOTE I (SI) after Step 14.
k = 0.343
k = 0.343
kd = (0.343)(21.5 in.) = 7.37 in.
kd = (0.343)(546.1 mm) = 187 mm
Calculate the stress level in the reinforcing
steel using Eq. (10-14) and verify that it is less
than the recommended limit per Eq. (10-6).
Ms + ε bi A f E f ( d f – kd
------) ( d – kd )E s
3
fs,s= -------------------------------------------------------------------------------------------------------------------------------kd
------ ) ( d f – kd )
A s E s ( d – ------ ) ( d – kd ) + A f E f ( d f – kd
3
3
fs,s ≤ 0.80fy
†
See EQUATION NOTE II (U.S.) after Step 14.
††
See EQUATION NOTE II (SI) after Step 14.
fs,s = 40.4 ksi ≤ (0.80)(60 ksi) = 48 ksi
fs,s = 279 N/mm2 ≤ (0.80)(410 N/mm2) = 330 N/mm2
∴ the stress level in the reinforcing steel is within the
recommended limit.
∴ the stress level in the reinforcing steel is within the
recommended limit.
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Procedure
440.2R-47
Calculation in inch-pound units
Calculation in SI metric units
E d f – kd⎞
ff,s = fs,s ⎛ -----f⎞ ⎛ --------------- – ε bi E f
⎝ E s⎠ ⎝ d – kd ⎠
5360 ksi -⎞ ⎛ ----------------------------------------24 in. – 7.37 in. -⎞
f f, s = 40.4 ksi ⎛ -----------------------⎝ 29,000 ksi⎠ ⎝ 21.5 in. – 7.37 in.⎠
2 37 kN/mm ⎞ ⎛ 609.6 mm – 187 mm⎞
f f, s = 0.278 kN/mm ⎛ -----------------------------⎝ 200 kN/mm 2⎠ ⎝ ------------------------------------------------546 mm – 187 mm ⎠
For a carbon FRP system, the sustained plus
cyclic stress limit is obtained from Table 10.1:
– (0.00061)(5360 ksi)
– (0.00061)(38 N/mm2)
Sustained plus cyclic stress limit = 0.55ffu
ff,s = 5.60 ksi ≤ (0.55)(85 ksi) = 47 ksi
ff,s = 38 N/mm2 ≤ (0.55)(590 N/mm2) = 324 N/mm2
∴ the stress level in the FRP is within the
recommended sustained plus cyclic stress limit.
∴ the stress level in the FRP is within the
recommended sustained plus cyclic stress limit.
Step 14—Check creep rupture limit at
service of the FRP
Calculate the stress level in the FRP using
Eq. (10-15) and verify that it is less than
creep-rupture stress limit given in
Table 10.1. Assume that the full service load
is sustained.
*
EQUATION NOTE I (U.S.):
k =
**
2
29,000
24 in. -⎞ ⎞ ⎛
⎛ 0.0116 ⎛ 29,000
----------------⎞ + 0.00372 ⎛ 5360
------------⎞ ⎞ + 2 ⎛ 0.0116 ⎛ ----------------⎞ + 0.00372 ⎛ 5360
------------⎞ ⎛ ----------------0.0116 ⎛ 29,000
----------------⎞ + 0.00372 ⎛ 5360
------------⎞ ⎞
⎝ 4030 ⎠
⎝ 4030 ⎠
⎝ 4030⎠ ⎠
⎝ 4030⎠ ⎝ 21.5 in.⎠ ⎠ – ⎝
⎝
⎝
⎝ 4030 ⎠
⎝ 4030⎠ ⎠
EQUATION NOTE I (SI):
k =
†
2
200 ⎞ + 0.00372 ⎛ 37 ⎞ ⎞ 2 + 2 ⎛ 0.0116 ⎛ 200 ⎞ + 0.00372 ⎛ 37 ⎞ ⎛ 609.6 mm⎞ ⎞ – ⎛ 0.0116 ⎛ 200 ⎞ + 0.00372 ⎛ 37 ⎞ ⎞
⎛ 0.0116 ⎛ ------------------------------------ -----------------------------------------⎝
⎝ 27.6⎠
⎝ 27.6⎠ ⎠
⎝
⎝ 27.6⎠
⎝ 27.6⎠ ⎝ 546 mm ⎠ ⎠ ⎝
⎝ 27.6⎠
⎝ 27.6⎠ ⎠
EQUATION NOTE II (U.S.):
2
7.37 in.
2424 k-in. + ( 0.00061 ) ( 0.96 in. ) ( 5360 ksi ) ⎛ 24 in. – ------------------⎞ (21.5 in. – 7.37 in.) ( 29,000 ksi )
⎝
3 ⎠
fs,s = ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2
in.-⎞ (21.5 in. – 7.37 in.) + ( 0.96 in. 2 ) ( 5360 ksi ) ⎛ 24 in. – 7.37
in.-⎞ ( 24 in. – 7.37 in. )
( 3.00 in. ) ( 29,000 ksi ) ⎛ 21.5 in. – 7.37
--------------------------------⎝
⎝
3 ⎠
3 ⎠
††
EQUATION NOTE II (SI):
2
2
2
187 mm
273,912 kN-mm + ( 0.00061 ) ( 619 mm ) ( 37 kN/mm ) ⎛ 609.6 mm – -------------------⎞ ( 546 mm – 187 mm ) ( 200 kN/mm )
⎝
3 ⎠
fs,s = ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2
2
mm⎞ ( 546 mm – 187 mm ) + ( 619 mm 2 ) ( 37 kN/mm 2 ) ⎛ 607 mm – 187
mm⎞ ( 607 mm – 187 mm )
( 1935 mm ) ( 200 kN/mm ) ⎛ 546 mm – 187
------------------------------------⎝
⎝
3 ⎠
3 ⎠
In detailing the FRP reinforcement, the FRP should be terminated a minimum of ldf , calculated per Eq. (13-2), past the point
on the moment diagram that represents cracking. The factored shear force at the termination should also be checked against the
shear force that causes FRP end peeling, estimated as 2/3 of the concrete shear strength. If the shear force is greater than 2/3 of
the concrete shear strength, the FRP strips should be extended further toward the supports. U-wraps may also be used to
reinforce against cover delamination.
15.4—Flexural strengthening of an interior reinforced concrete beam with NSM FRP bars
An existing reinforced concrete beam (Fig. 15.2) is to be strengthened using the loads given in Table 15.3 and the NSM FRP
system described in Table 15.5. Specifically, three No. 3 CFRP bars are to be used at a distance 23.7 in. (602.1 mm) from the
extreme top fiber of the beam.
Table 15.5—Manufacturer’s reported NSM FRP
system properties
Fig. 15.2—Schematic of the idealized simply supported
beam with FRP external reinforcement.
Area per No. 3 bar
0.10 in.2
64.5 mm2
Ultimate tensile strength ffu*
250 ksi
1725 N/mm2
Rupture strain εfu*
0.013 in./in.
0.013 mm/mm
Modulus of elasticity of
FRP laminates Ef
19,230 ksi
132,700 N/mm2
440.2R-48
ACI COMMITTEE REPORT
By inspection, the level of strengthening is reasonable in that it does meet the strengthening limit criteria put forth in Eq. (10-1).
That is, the existing flexural strength without FRP, (φMn)w/o = 266 k-ft (361 kN-m), is greater than the unstrengthened moment
limit, (1.1MDL + 0.75MLL )new = 177 k-ft (240 kN-m). The design calculations used to verify this configuration follow.
Procedure
Calculation in inch-pound units
Calculation in SI metric units
ffu = (0.95)(250 ksi) = 237.5 ksi
εfu = (0.95)(0.013 in./in.) = 0.0123 in./in.
ffu = (0.95)(1725 N/mm2) = 1639 N/mm2
εfu = (0.95)(0.013 mm/mm) = 0.0123 mm/mm
β1 from ACI 318-05, Section 10.2.7.3
f c′
β1 = 1.05 – 0.05 ----------- = 0.85
1000
f c′
β1 = 1.05 – 0.05 ------ = 0.85
6.9
Ec = 57,000√fc′
E c = 57,000 5000 psi = 4,030,000 psi
E c = 4700 34.5 N/mm = 27,600 N/mm2
As = 3(1.00 in.2) = 3.00 in.2
As = 3(645.2 mm2) = 1935 mm2
Af = (3 bars)(0.01 in.2/bar) = 0.3 in.2
Af = (3 bars)(64.5 mm2/bar) = 194 mm2
( 864 k-in. ) [ 23.7 in. – ( 0.334 ) ( 21.5 in. ) ]
ε bi = ------------------------------------------------------------------------------------------------4
( 5937 in. ) ( 4030 ksi )
( 97.6 kN-mm ) [ 602 mm – ( 0.334 ) ( 546 mm ) ]
εbi = ------------------------------------------------------------------------------------------------------------6
4
2
( 2471 × 10 mm ) ( 27.6 kN/mm )
εbi = 0.00061
εbi = 0.00061
κm = 0.7
κm = 0.7
c = (0.20)(21.5 in.) = 4.30 in.
c = (0.20)(546 mm) = 109 mm
d f – c⎞
– εbi ≤ κmεfd
εfe = 0.003 ⎛ -----------⎝ c ⎠
in. – 4.3 in.-⎞ – 0.00061
εfe = 0.003 ⎛ 23.7
-------------------------------------= 0.0129
⎝
⎠
4.3 in.
602 mm – 109 mm
εfe = 0.003 ⎛ ---------------------------------------------⎞ – 0.00061 = 0.0129
⎝
⎠
109 mm
Note that for the neutral axis depth selected,
FRP debonding would be the failure mode
because the second expression in this equation controls. If the first expression
governed, then concrete crushing would be
the failure mode.
κmεfd = 0.7(0.0123) = 0.00865
κmεfd = 0.7(0.0123) = 0.00865
Hence, εfe = 0.00865
(Mode of failure is FRP debonding)
Hence, εfe = 0.00865
(Mode of failure is FRP debonding)
4.3
εc = (0.00865 + 0.00061) ⎛ ------------------------⎞ = 0.0020
⎝ 23.7 – 4.3⎠
109
εc = (0.00865 + 0.00061) ⎛ ------------------------⎞ = 0.0020
⎝ 602 – 109⎠
Step 1—Calculate the FRP system design
material properties
The beam is located in an interior space and
a CFRP material will be used. Therefore,
per Table 9.1, an environmental reduction
factor of 0.95 is suggested.
ffu = CE ffu*
εfu = CEεfu*
Step 2—Preliminary calculations
Properties of the concrete:
2
Step 3—Determine the existing state of
strain on the soffit
The existing state of strain is calculated
assuming the beam is cracked and the only
loads acting on the beam at the time of the FRP
installation are dead loads. A cracked section
analysis of the existing beam gives k = 0.334
and Icr = 5937 in.4 = 2471 × 106 mm4
M DL ( d f – kd )
ε bi = ------------------------------I cr E c
Step 4—Determine the bond-dependent
coefficient of the FRP system
Based on the manufacturer’s recommendation, the dimensionless bond-dependent
coefficient for flexure κm is 0.7.
Step 5—Estimate c, the depth to the
neutral axis
A reasonable initial estimate of c is 0.20d.
The value of the c is adjusted after checking
equilibrium.
c = 0.20d
Step 6—Determine the effective level of
strain in the FRP reinforcement
The effective strain level in the FRP may be
found from Eq. (10-3).
Because FRP controls the failure of the
section, the concrete strain at failure, εc ,
may be less than 0.003 and can be calculated
using similar triangles:
c
εc = (εfd + εbi) ⎛ ------------⎞
⎝ d f – c⎠
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Procedure
440.2R-49
Calculation in inch-pound units
Calculation in SI metric units
21.5 – 4.3
εs = (0.00865 + 0.00061) ⎛ ------------------------⎞ = 0.0082
⎝ 23.7 – 4.3⎠
546 – 109
εs = (0.00865 + 0.00061) ⎛ ------------------------⎞ = 0.0082
⎝ 602 – 109⎠
fs = Esεs ≤ fy
fs = (29,000 ksi)(0.0082) ≤ 60 ksi
fs = 238 ksi ≤ 60 ksi
Hence, fs = 60 ksi
fs = (200 kN/mm2)(0.0082) ≤ 0.414 kN/mm2
fs = 1.64 kN/mm2 ≤ 0.414 kN/mm2
Hence, fs = 0.414 kN/mm2
ffe = Ef εfe
ffe = (19,230 ksi)(0.00865) = 166 ksi
ffe = (132,700 N/mm2)(0.00865) = 1147 N/mm2
Step 9—Calculate the internal force
resultants and check equilibrium
Concrete stress block factors may be calculated using ACI 318-05. Approximate stress
block factors may also be calculated based
on the parabolic stress-strain relationship for
concrete as follows:
1.7 ( 5000 )- = 0.0021
ε c′ = ------------------------6
4030 × 10
( 34.5 )- = 0.0021
ε c′ = 1.7
---------------------27,606
4ε′c – ε c
β 1 = ----------------------6ε′c – 2ε c
4 ( 0.0021 ) – 0.002
β 1 = ---------------------------------------------------- = 0.743
6 ( 0.0021 ) – 2 ( 0.002 )
4 ( 0.0021 ) – 0.002
β 1 = ---------------------------------------------------- = 0.743
6 ( 0.0021 ) – 2 ( 0.002 )
Step 7—Calculate the strain in the existing
reinforcing steel
The strain in the reinforcing steel can be
calculated using similar triangles according to
Eq. (10-10).
d–c
εs = (εfe + εbi)⎛ ------------⎞
⎝ d f – c⎠
Step 8—Calculate the stress level in the
reinforcing steel and FRP
The stresses are calculated using Eq. (10-11)
and (10-9).
2
3ε′c ε c – ε c
α 1 = -----------------------2
3β 1 ε c′
2
3 ( 0.0021 ) ( 0.002 ) – ( 0.002 )
α 1 = --------------------------------------------------------------------- = 0.870
2
3 ( 0.743 ) ( 0.0021 )
2
( 0.0021 ) ( 0.002 ) – ( 0.002 )- = 0.870
α 1 = 3--------------------------------------------------------------------2
3 ( 0.743 ) ( 0.0021 )
where εc′ is strain corresponding to fc′ calculated as
1.7f c′
ε c′ = -----------Ec
Force equilibrium is verified by checking the
initial estimate of c with Eq. (10-12).
c=
A s f s + A f f fe
c = ------------------------α 1 f c′ β 1 b
2
2
( 3.00 in. ) ( 60 ksi ) + ( 0.3 in. ) ( 166 ksi )c = ----------------------------------------------------------------------------------------------( 0.87 ) ( 5 ksi ) ( 0.743 ) ( 12 in. )
c = 5.92 in. ≠ 4.30 in. n.g.
∴ Revise estimate of c and repeat Steps 6 through 9
until equilibrium is achieved.
Step 10—Adjust c until force equilibrium
is satisfied
Steps 6 through 9 were repeated several
times with different values of c until equilibrium was achieved. The results of the final
iteration are
c = 5.26 in.; εs = 0.0082; fs = fy = 60 ksi;
εfe = 0.00865; εc = 0.0027; β1 = 0.786;
α1 = 0.928; and ffe = 166 ksi
2
2
2
2
2
2
(1935 mm ) ( 414 N/mm ) + ( 194 mm ) ( 1147 N/mm )
-----------------------------------------------------------------------------------------------------------------------------------2
( 0.87 ) ( 34.5 N/mm ) ( 0.743 ) ( 305 mm )
c = 150 mm ≠ 109 in. n.g.
∴ Revise estimate of c and repeat Steps 6 through 9
until equilibrium is achieved.
2
2
2
2
( 3.00 in. ) ( 60 ksi ) + ( 0.3 in. ) ( 166 ksi )
c = -----------------------------------------------------------------------------------------------( 0.928 ) ( 5 ksi ) ( 0.786 ) ( 12 in. )
c = ----------------------------------------------------------------------------------------------------------------------------------------
c = 5.25 in. ≈ 5.26 in. ✓ OK
c = 133 mm ≈ 134 mm ✓ OK
∴ the value of c selected for the final iteration is correct.
∴ the value of c selected for the final iteration is correct.
(1935 mm ) ( 414 N/mm ) + ( 193 mm ) ( 1147 N/mm )
2
( 0.928 ) ( 34.5 N/mm ) ( 0.786 ) ( 305 mm )
440.2R-50
ACI COMMITTEE REPORT
Procedure
Calculation in inch-pound units
Calculation in SI metric units
2
0.786 ( 5.25 in. )
M ns = ( 3.0 in. ) ( 60 ksi ) ⎛ 21.5 in. – -------------------------------------⎞
⎝
⎠
2
2
2
0.786 ( 133 mm )
M ns = ( 1935 mm ) ( 414 N/mm ) ⎛ 546 mm – --------------------------------------⎞
⎝
⎠
2
Mns = 3498 k-in. = 291 k-ft
Mns = 394 kN-m
Step 11—Calculate flexural strength
components
The design flexural strength is calculated
using Eq. (10-13). An additional reduction
factor, ψf = 0.85, is applied to the contribution of the FRP system.
Steel contribution to bending:
β 1 c⎞
M ns = A s f s ⎛ d – ------⎝
2 ⎠
FRP contribution to bending:
2
2 ⎛
0.786 ( 133 mm )⎞
2
0.786 ( 5.25 in. )
-⎠
M nf = ( 0.3 in. ) ( 166 ksi ) ⎛ 23.7 in. – -------------------------------------⎞ Mnf = ( 194 mm ) ( 1147 N/mm ) ⎝ 602.1 mm – ------------------------------------2
⎝
⎠
2
β 1 c⎞
M nf = A f f fe ⎛ d f – ------⎝
2 ⎠
Mnf = 1077 k-in. = 90 k-ft
Mnf = 122 kN-m
φMn = 0.9[291 k-ft + 0.85(90 k-ft)]
φMn = 331 k-ft ≥ Mu = 294 k-ft
φMn = 0.9[394 kN-m + 0.85(122 kN-m)]
φMn = 448 kN-m ≥ Mu = 398 kN-m
∴ the strengthened section is capable of sustaining
the new required flexural strength.
∴ the strengthened section is capable of sustaining
the new required flexural strength.
Step 12—Calculate design flexural
strength of the section
The design flexural strength is calculated
using Eq. (10-1) and (10-13). Because εs =
0.0082 > 0.005, a strength reduction factor
of φ = 0.90 is appropriate per Eq. (10-5).
φMn = φ[Mns + ψf Mnf ]
Step 13—Check service stresses in the
reinforcing steel and the FRP
Calculate the elastic depth to the cracked
neutral axis. This can be simplified for a rectangular beam without compression reinforcement as follows:
k =
Es
E 2
E
E d
⎛ ρ ---- + ρ f -----f ⎞ + 2 ⎛ ρ s -----s + ρ f -----f ⎛ ----f⎞ ⎞
⎝ s Ec
⎝ Ec
E c⎠
Ec ⎝ d ⎠ ⎠
*
E
E
– ⎛ ρ s -----s + ρ f -----f ⎞
⎝ Ec
E c⎠
See EQUATION NOTE I (U.S.) after Step 14.
**
See EQUATION NOTE I (SI) after Step 14.
k = 0.345
k = 0.345
kd = (0.345)(21.5 in.) = 7.4 in.
kd = (0.345)(546 mm) = 188 mm
Calculate the stress level in the reinforcing
steel using Eq. (10-14) and verify that it is less
than the recommended limit per Eq. (10-6).
Ms + ε bi A f E f ( d f – kd
------) ( d – kd )E s
3
fs,s= ------------------------------------------------------------------------------------------------------------------------------kd
------ ) ( d f – kd )
A s E s ( d – ------ ) ( d – kd ) + A f E f ( d f – kd
3
3
fs,s ≤ 0.80fy
†
See EQUATION NOTE II (U.S.) after Step 14.
††
See EQUATION NOTE II (SI) after Step 14.
fs,s = 40.3 ksi ≤ (0.80)(60 ksi) = 48 ksi
fs,s = 278 N/mm2 ≤ (0.80)(410 N/mm2) = 330 N/mm2
∴ the stress level in the reinforcing steel is within the
recommended limit.
∴ the stress level in the reinforcing steel is within the
recommended limit.
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Procedure
440.2R-51
Calculation in inch-pound units
Calculation in SI metric units
E d f – kd⎞
ff,s = fs,s ⎛ -----f⎞ ⎛ --------------- – ε bi E f
⎝ E s⎠ ⎝ d – kd ⎠
ksi 23.7 in. – 7.4 in.
f f, s = 40.3 ksi ⎛ 19,230
-------------------------⎞ ⎛ ---------------------------------------⎞
⎝ 29,000 ksi⎠ ⎝ 21.5 in. – 7.4 in.⎠
2
kN/mm ⎞ ⎛ 602 mm – 188 mm⎞
f f, s = 0.278 kN/mm ⎛ 133
- ---------------------------------------------2
⎝ -----------------------------200 kN/mm ⎠ ⎝ 546 mm – 188 mm⎠
For a carbon FRP system, the sustained plus
cyclic stress limit is obtained from Table 10.1:
– (0.00061)(19,230 ksi)
– (0.00061)(133 N/mm2)
Sustained plus cyclic stress limit = 0.55ffu
ff,s = 19 ksi ≤ (0.55)(85 ksi) = 50 ksi
ff,s = 134 N/mm2 ≤ (0.55)(590 N/mm2) = 324.5 N/mm2
∴ the stress level in the FRP is within the
recommended sustained plus cyclic stress limit.
∴ the stress level in the FRP is within the
recommended sustained plus cyclic stress limit.
Step 14—Check creep rupture limit at
service of the FRP
Calculate the stress level in the FRP using
Eq. (10-15) and verify that it is less than
creep-rupture stress limit given in
Table 10.1. Assume that the full service load
is sustained.
2
*
EQUATION NOTE I (U.S.):
k =
2
in.-⎞ ⎞ – ⎛ 0.0116 ⎛ 29,000
⎛ 0.0116 ⎛ 29,000
----------------⎞ + 0.0012 ⎛ 19,230
----------------⎞ ⎞ + 2 ⎛ 0.0116 ⎛ 29,000
----------------⎞ + 0.0012 ⎛ 19,230
----------------⎞ ⎛ 23.7
--------------------------------⎞ + 0.0012 ⎛ 19,230
----------------⎞ ⎞
⎝
⎝ 4030 ⎠
⎝ 4030 ⎠ ⎠
⎝
⎝ 4030 ⎠
⎝ 4030 ⎠ ⎝ 21.5 in. ⎠ ⎠ ⎝
⎝ 4030 ⎠
⎝ 4030 ⎠ ⎠
**
EQUATION NOTE I (SI):
k =
200 ⎞ + 0.0012 ⎛ 133 ⎞ ⎞ 2 + 2 ⎛ 0.0116 ⎛ 200 ⎞ + 0.0012 ⎛ 133 ⎞ ⎛ 602 mm⎞ ⎞ – ⎛ 0.0116 ⎛ 200 ⎞ + 0.0012 ⎛ 133 ⎞ ⎞
⎛ 0.0116 ⎛ ------------------------------------ -------------------------------------⎝
⎝ 27.6⎠
⎝ 27.6⎠ ⎠
⎝
⎝ 27.6⎠
⎝ 27.6⎠ ⎝ 546 mm⎠ ⎠ ⎝
⎝ 27.6⎠
⎝ 27.6⎠ ⎠
†
EQUATION NOTE II (U.S.):
2
7.4 in.
2424 k-in. + ( 0.00061 ) ( 0.3 in. ) ( 19,230 ksi ) ⎛ 23.7 in. – ---------------⎞ (21.5 in. – 7.4 in.) ( 29,000 ksi )
⎝
3 ⎠
fs,s = ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2
2
in.-⎞ (21.5 in. – 7.4 in.) + ( 0.3 in. ) ( 19,230 ksi ) ⎛ 23.7 in. – 7.4
in.-⎞ ( 23.7 in. – 7.4 in. )
( 3.00 in. ) ( 29,000 ksi ) ⎛ 21.5 in. – 7.4
--------------------------⎝
⎝
3 ⎠
3 ⎠
††
EQUATION NOTE II (SI):
2
2
2
188 mm
273,912 kN-mm + ( 0.00061 ) ( 194 mm ) ( 132.7 kN/mm ) ⎛ 602 mm – -------------------⎞ ( 546 mm – 188 mm ) ( 200 kN/mm )
⎝
3 ⎠
fs,s = -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------2
2
mm⎞ ( 546 mm – 188 mm ) + ( 194 mm 2 ) ( 132.7 kN/mm 2 ) ⎛ 602 mm – 188
mm⎞ ( 602 mm – 188 mm )
( 1935 mm ) ( 200 kN/mm ) ⎛ 546 mm – 188
------------------------------------⎝
⎝
3 ⎠
3 ⎠
In detailing the FRP reinforcement, FRP bars should be terminated at a distance equal to the bar development length past the
point on the moment diagram that represents cracking.
440.2R-52
ACI COMMITTEE REPORT
15.5—Flexural strengthening of an interior prestressed concrete beam with FRP laminates
A number of continuous prestressed concrete beams with five 1/2 in. (12.7 mm) diameter bonded strands (Fig. 15.3) are
located in a parking garage that is being converted to an office space. All prestressing strands are Grade 270 ksi (1860 N/mm2) lowrelaxation seven-wire strands. The beams require an increase in their live-load-carrying capacity from 50 lb/ft2 (244 kg/m2) to 75 lb/ft2
(366 kg/m2). The beams are also required to support an additional dead load of 10 lb/ft2. Analysis indicates that each existing
beam has adequate flexural capacity to carry the new loads in the negative moment region at the supports but is deficient in
flexure at midspan and in shear at the supports. The beam meets the deflection and crack control serviceability requirements.
The cast-in-place beams support a 4 in. (100 mm) slab. For bending at midspan, beams should be treated as T-sections. Summarized
in Table 15.6 are the existing and new loads and associated midspan moments for the beam. FRP system properties are shown
in Table 15.4, shown again on this page for convenience.
Length of the beam l
29 ft
Bay width l2
30 ft
9.14 m
Width of beam w
dp
24 in.
610 mm
22.5 in.
571 mm
Effective flange width bf
25 in.
87 in.
635 mm
2210 mm
Flange thickness hf
4 in.
102 mm
fc′
4000 psi
h
Fig. 15.3—Schematic of the idealized continuous prestressed
beam with FRP external reinforcement.
8.84 m
Strands diameter
1/2 in.
27.6 N/mm2
12.7 mm
fpe
165 ksi
1138 N/mm2
fpy
230 ksi
1586 N/mm2
fpu
270 ksi
1860 N/mm2
Ep
28,500 ksi
1.96 × 105 N/mm2
φMn without FRP
336 k-ft
455 kN-m
Table 15.6—Loadings and corresponding moments
Loading/moment
Dead loads wDL
2.77 k/ft
Existing loads
40.4 N/mm
3.09 k/ft
Anticipated loads
45.1 N/mm
Live load wLL
1.60 k/ft
23.3 N/mm
2.4 k/ft
35 N/mm
80.2 N/mm
Unfactored loads (wDL + wLL )
4.37 k/ft
63.8 N/mm
5.49 k/ft
Unstrengthened load limit (1.1wDL + 0.75wLL )
N/A
N/A
5.2 k/ft
75.9 N/mm
Factored loads (1.2wDL + 1.6wLL )
5.88 k/ft
85.9 N/mm
7.55 k/ft
110.2 N/mm
Dead-load moment MDL
147 k-ft
199 kN-m
162 k-ft
220.2 kN-m
Live-load moment MLL
85 k-ft
115 kN-m
126 k-ft
171.1 kN-m
Service-load moment Ms
232 k-ft
314 kN-m
288 k-ft
391.3 kN-m
Unstrengthened moment limit (1.1MDL + 0.75MLL)new
N/A
N/A
273 k-ft
371 kN-m
Factored moment Mu
312 k-ft
423 kN-m
397 k-ft
538 kN-m
By inspection, the level of strengthening is reasonable in that it does meet the strengthening limit criteria put forth in Eq. (10-1).
That is, the existing flexural strength without FRP, (φMn)w/o = 336 k-ft (455 kN-m), is greater than the unstrengthened moment
limit, (1.1MDL + 0.75MLL )new = 273 k-ft (370 kN-m). The design calculations used to verify this configuration follow. The
beam is to be strengthened using the FRP system described in Table 15.4. A one-ply, 24 in. (610 mm) wide strip of FRP is
considered for this evaluation.
Table 15.4—Manufacturer’s reported FRP system properties
Thickness per ply tf
0.040 in.
1.02 mm
Ultimate tensile strength ffu*
90 ksi
621 N/mm2
0.015 in./in.
0.015 mm/mm
5360 ksi
37,000 N/mm2
Rupture strain εfu*
Modulus of elasticity of FRP laminates Ef
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Procedure
440.2R-53
Calculation in inch-pound units
Calculation in SI metric units
ffu = (0.95)(90 ksi) = 85 ksi
εfu = (0.95)(0.015 in./in.) = 0.0142 in./in.
ffu = (0.95)(621 N/mm2) = 590 N/mm2
εfu = (0.95)(0.015 mm/mm) = 0.0142 mm/mm
β1 from ACI 318-05, Section 10.2.7.3
f c′
β1 = 1.05 – 0.05 ----------- = 0.85
1000
f c′
β1 = 1.05 – 0.05 ------ = 0.85
6.9
Ec = 57,000√fc′
E c = 57,000 4000 psi = 3,605,000 psi
E c = 4700 27.6 N/mm = 24,700 N/mm2
Aps = 5(0.153 in.2) = 0.765 in.2
Aps = 5(99 mm2) = 495 mm2
Af = (1 ply)(0.040 in./ply)(24 in.) = 0.96 in.2
Af = (1 ply)(1.0 mm/ply)(610 mm) = 610 mm2
Acg = (87 in.)(4 in.) + (24 in.)(25 in. – 4 in.) = 852 in.2
Acg = (2210 mm)(102 mm)
+ (610 mm)(612 mm – 102 mm) = 5.5 × 105 mm2
Step 1—Calculate the FRP-system design
material properties
The beam is located in an interior space and
a CFRP material will be used. Therefore,
per Table 9.1, an environmental reduction
factor of 0.95 is suggested.
ffu = CE ffu*
εfu = CEεfu*
Step 2—Preliminary calculations
Properties of the concrete:
2
Properties of the existing prestressing steel:
Area of FRP reinforcement:
Af = ntf wf
Cross-sectional area:
Acg = behf + bw(h – hf )
Distance from the top fiber to the section
centroid:
2
4 in.
87 in. × ----------- + 24 in. × 21 × 14.5
2
y t = ---------------------------------------------------------------------------------- = 9.39 in.
852
2
( h – h f )⎞
h
b f -----f + b w ( h – h f ) ⎛ h f + ----------------⎝
2 ⎠
2
y t = --------------------------------------------------------------------------A cg
2
102 mm
2210 mm × --------------------- + 610 mm × 533 × 368
2
y t = ----------------------------------------------------------------------------------------------------------5
5.5 × 10
= 238 mm
Gross moment of inertia:
3
bf hf
h
I g = --------+ b f h f ⎛ y t – ----f⎞
⎝
12
2⎠
3
2
3
bw ( h – hf )
h–h
+ ------------------------- + b w ( h – h f ) ⎛ y t – -------------f⎞
⎝
2 ⎠
12
2
87 in. × 4 in.
I g = --------------------------------- + 87 in. × 4 in. ( 9.39 in. – 2 )
12
2
3
in. × 21 - + 24 in. × 21 ( 9.39 – 14.5 ) 2 = 51,150 in. 4
+ 24
--------------------------12
3
mm × 102 mm - + 2210 mm × 102 mm ( 238 – 51 ) 2
I g = 2210
-------------------------------------------------12
3
2
10
610 mm × 533
+ -------------------------------------+ 610 mm × 533 ( 238 – 368 ) = 2.13 × 10 mm
12
Radius of gyration:
r =
I
------gA cg
r =
51,150
---------------- = 7.75 in.
852
10
r =
2.13 × 10
------------------------- = 197 mm
5
5.5 × 10
Effective prestressing strain:
f pe
ε pe = ---Ep
265
ε pe = ---------------- = 0.00589
28,500
1138
ε pe = ------------------------5 = 0.00589
1.96 × 10
Pe = 0.765 × 165 = 126.2 kips
Pe = 495 × 1138 = 563,310 N
e = 22.5 – 9.39 = 13.1 in.
e = 571 – 238 = 333 mm
yb = 25 – 9.39 = 15.61 in.
yb = 635 – 238 = 397 mm
Effective prestressing force:
Pe = Aps fpe
Eccentricity of prestressing force:
e = dp – yt
Step 3—Determine the existing state of
strain on the soffit
The existing state of strain is calculated
assuming the beam is uncracked and the only
loads acting on the beam at the time of the FRP
installation are dead loads.
Distance from extreme bottom fiber to the
section centroid:
yb = h – yt
Initial strain in the beam soffit:
ey b⎞ M DL y b
–pe ⎛
ε bi = ------------ 1 + ------+ --------------2
Ec Ig
E c A cg ⎝
r ⎠
6
– 126.2 ⎛ 1 + 13.1
× 15.6-⎞ 147 × 12 × 15.6
– 563,310
333 × 397⎞
199 × 10 × 397
⎛
ε bi = --------------------------------------------------+ -------------------------------------- + -------------------------------------------------2
⎠ 3605 × 51,150 ε bi = --------------------------------------------5- ⎝ 1 + ----------------------2 ⎠
10
3605 × 852 ⎝
7.75
24,700 × 5.5 × 10
24,700 × 2.13 × 10
197
εbi = –3 × 10–5
εbi = –3 × 10–5
440.2R-54
ACI COMMITTEE REPORT
Procedure
Calculation in inch-pound units
Calculation in SI metric units
4000 psi
ε fd = 0.083 --------------------------------------------------------------1 ( 5,360,000 psi ) ( 0.04 in. )
27.6 N/mm
ε fd = 0.042 -----------------------------------------------------------------------2
1 ( 37,000 N/mm ) ( 1.016 mm )
= 0.0113 ≤ 0.9(0.0142) = 0.0128
= 0.0113 ≤ 0.9(0.0142) = 0.0128
c = 0.1h
Step 6—Determine the effective level of
strain in the FRP reinforcement
The effective strain level in the FRP may be
found from Eq. (10-3).
c = (0.1)(25 in.) = 2.50 in.
c = (0.1)(635 mm) = 63.5 mm
d f – c⎞
– εbi ≤ εfd
εfe = 0.003 ⎛ -----------⎝ c ⎠
25 – 2.5
εfe = 0.003 ⎛ -------------------⎞ – 0.00003 = 0.027
⎝ 2.5 ⎠
635 – 63.5
εfe = 0.003 ⎛ -------------------------⎞ – 0.00003 = 0.027
⎝ 63.5 ⎠
Note that for the neutral axis depth selected,
FRP debonding would be the failure mode
because the second expression in this equation controls. If the first (limiting) expression
governed, then FRP rupture would be the
failure mode.
> εfd = 0.0113
εfd = 0.0113
Failure is governed by FRP debonding
Failure is governed by FRP debonding
εfe = εfd = 0.0113
εfe = εfd = 0.0113
– 2.5
εpnet = (0.0113 + 0.00003) ⎛ 22.5
------------------------⎞
⎝ 25 – 2.5 ⎠
– 63.5
εpnet = (0.0113 + 0.00003)⎛ 571
-------------------------⎞
⎝ 635 – 63.5⎠
εpnet = 0.01
εpnet = 0.01
Step 4—Determine the design strain of the
FRP system
The design strain of FRP accounting for
debonding failure mode εfd is calculated
using Eq. (10-2)
2
Because the design strain is smaller than the
rupture strain, debonding controls the
design of the FRP system.
Step 5—Estimate c, the depth to the
neutral axis
A reasonable initial estimate of c is 0.1h.
The value of the c is adjusted after checking
equilibrium.
Step 7—Calculate the strain in the existing
prestressing steel
The strain in the prestressing steel can be
calculated using Eq. (10-23b) and (10-22).
d p – c⎞
εpnet = (εfe + εbi) ⎛ -----------⎝ df – c ⎠
2
Pe ⎛
e
ε ps = ε pe + ---------- 1 + ---2-⎞ + ε pnet ≤ 0.035
Ac Ec ⎝
r⎠
2
2
126.2 - ⎛ 1 + ----------13.1-⎞ + 0.01
ε ps = 0.00589 + -------------------------2
852 × 3605 ⎝
7.75 ⎠
563,310
- ⎛ 1 + 333
ε ps = 0.00589 + -----------------------------------------------------2⎞ + 0.01
5
197 ⎠
5.5 × 10 × 24,700 ⎝
εps = 0.016 ≤ 0.035
εps = 0.016 ≤ 0.035
⎧
28,500ε ps for ε ps ≤ 0.0086
⎪
fps = ⎨
0.04 - for ε > 0.0086
ps
⎪ 270 – ------------------------ε ps – 0.007
⎩
0.04
fps = 270 – -------------------------------- = 265.6 ksi
0.016 – 0.007
0.276
fps = 1860 – --------------------------------- = 1831 N/mm2
0.016 – 0.007
ffe = Ef εfe
ffe = (5360 ksi)(0.0113) =60.6 ksi
ffe = (37,000 N/mm2)(0.0113) = 418 N/mm2
Step 8—Calculate the stress level in the
prestressing steel and FRP
The stresses are calculated using Eq. (10-24b)
and (10-21).
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Procedure
440.2R-55
Calculation in inch-pound units
Calculation in SI metric units
c ⎞
ε c = ( ε fe + ε bi ) ⎛ -----------⎝ d f – c⎠
2.5 ⎞ = 0.0013
ε c = ( 0.0113 + 0.00003 ) ⎛ -----------------⎝ 25 – 2.5⎠
63.5 ⎞ = 0.0013
ε c = ( 0.0113 + 0.00003 ) ⎛ -----------------------⎝ 635 – 63.5⎠
The strain εc′ corresponding to fc′ is calculated
as
1.7f c′
ε c′ = -----------Ec
1.7 ( 4000 )- = 0.0019
ε c′ = ------------------------6
3605 × 10
( 27.6 )- = 0.0019
ε c′ = 1.7
---------------------24,700
4 ( 0.0019 ) – 0.0013
β 1 = ------------------------------------------------------- = 0.716
6 ( 0.0019 ) – 2 ( 0.0013 )
4 ( 0.0019 ) – 0.0013
β 1 = ------------------------------------------------------- = 0.716
6 ( 0.0019 ) – 2 ( 0.0013 )
Step 9—Calculate the equivalent concrete
compressive stress block parameters α1
and β1
The strain in concrete at failure can be calculated from strain compatibility as follows:
Concrete stress block factors can be
estimated using ACI 318-05. Approximate
stress block factors may be calculated from
the parabolic stress-strain relationship for
concrete and is expressed as follows:
4ε′c – ε c
β 1 = ----------------------6ε′c – 2ε c
2
3ε′c ε c – ε c
α 1 = -----------------------2
3β 1 ε c′
( 0.0019 ) ( 0.0013 ) – ( 0.0013 )- = 0.738
α 1 = 3--------------------------------------------------------------------------2
3 ( 0.716 ) ( 0.0019 )
Step 10—Calculate the internal force
resultants and check equilibrium
Force equilibrium is verified by checking the
initial estimate of c with Eq. (10-25).
( 0.765 in. ) ( 265.6 ksi ) + ( 0.96 in. ) ( 60.6 ksi -)
c = --------------------------------------------------------------------------------------------------------------( 0.738 ) ( 4 ksi ) ( 0.716 ) ( 87 in. )
A p f ps + A f f fe
c = --------------------------α 1 f c′ β 1 b
c = 1.42 in. ≠ 2.50 in. n.g.
c = 36 mm ≠ 63.5 in. n.g.
∴ Revise estimate of c and repeat Steps 6 through 10
until equilibrium is achieved.
∴ Revise estimate of c and repeat Steps 6 through 10
until equilibrium is achieved.
2
2
3 ( 0.0019 ) ( 0.0013 ) – ( 0.0013 )
α 1 = --------------------------------------------------------------------------- = 0.738
2
3 ( 0.716 ) ( 0.0019 )
c=
2
2
Step 11—Adjust c until force equilibrium
2
2
is satisfied
( 0.765 in. ) ( 265.6 ksi ) + ( 0.96 in. ) ( 60.6 ksi )c = ---------------------------------------------------------------------------------------------------------------Steps 6 through 10 were repeated several
( 0.577 ) ( 4 ksi ) ( 0.698 ) ( 87 in. )
times with different values of c until equilibrium was achieved. The results of the final
iteration are
c = 1.86 in. = 1.86 in. ✓ OK
c = 1.86 in.; εps = 0.016; fps = fy = 265.6 ksi;
εfe = 0.0113; ffe = 60.6 ksi; εc = 0.00091;
∴ the value of c selected for the final iteration is correct.
α1 = 0.577; and β1 = 0.698.
2
2
2
2
(495
mm ) ( 1831 N/mm ) + ( 620 mm ) ( 418 N/mm )--------------------------------------------------------------------------------------------------------------------------------2
( 0.738 ) ( 27.6 N/mm ) ( 0.716 ) ( 2210 mm )
2
2
2
2
(495 mm ) ( 1831 N/mm ) + ( 620 mm ) ( 418 N/mm )
c = -----------------------------------------------------------------------------------------------------------------------------------2
( 0.577 ) ( 27.6 N/mm ) ( 0.698 ) ( 2210 mm )
c = 47 mm = 47 mm ✓ OK
∴ the value of c selected for the final iteration is correct.
Step 12—Calculate flexural strength
components
The design flexural strength is calculated
using Eq. (10-26). An additional reduction
factor, ψf = 0.85, is applied to the contribution of the FRP system.
Prestressing steel contribution to bending:
β 1 c⎞
M np = A p f ps ⎛ d p – ------⎝
2 ⎠
2
0.70 ( 1.86 in. )
M np = ( 0.765 in. ) ( 265.6 ksi ) ⎛ 22.5 in. – ----------------------------------⎞
⎝
⎠
2
2
2
0.70 ( 47 mm )
M np = ( 495 mm ) ( 1830 N/mm ) ⎛ 571.5 mm – ---------------------------------⎞
⎝
⎠
2
Mnp = 4440 k-in. = 370 k-ft
Mnp = 501.6 × 106 N-mm = 501.6 kN-m
2
0.70 ( 1.86 in. )-⎞
M nf = ( 0.96 in. ) ( 60.6 ksi ) ⎛ 25 in. – --------------------------------⎝
⎠
2
2
2
0.70 ( 47 mm )
M nf = ( 620 mm ) ( 418 N/mm ) ⎛ 635 mm – ---------------------------------⎞
⎝
⎠
2
Mnf = 1417 k-in. = 118 k-ft
Mnf = 160.1 × 106 N-mm = 160.1 kN-m
FRP contribution to bending:
β 1 c⎞
M nf = A s f fe ⎛ d f – ------⎝
2 ⎠
440.2R-56
ACI COMMITTEE REPORT
Procedure
Calculation in inch-pound units
Calculation in SI metric units
φMn = 0.9[370 k-ft + 0.85(118 k-ft)]
φMn = 423 k-ft ≥ Mu = 397 k-ft
φMn = 0.9[506.1 kN-m + 0.85(160.1 kN-m)]
φMn = 573 kN-m ≥ Mu = 538 kN-m
∴ the strengthened section is capable of sustaining
the new required flexural strength.
∴ the strengthened section is capable of sustaining
the new required flexural strength.
f r = 7.5 4000 = 474 psi = 0.474 ksi
f r = 7.5 27.6 = 3.67 N/mm2
Step 13—Calculate design flexural
strength of the section
The design flexural strength is calculated
using Eq. (10-1) and (10-26). Because εps =
0.016 > 0.015, a strength reduction factor of
φ = 0.90 should be used per Eq. (10-5). An
additional reduction factor ψf = 0.85 is used
to calculate the FRP contribution to nominal
capacity.
φMn = φ[Mnp + ψf Mnf ]
Step 14—Check service condition of the
section
Calculate the cracking moment and compare
the service moment:
f r = 7.5 f c′
2
fr Ig
r -⎞
M cr = ------+ P e ⎛ e + --⎝
yb
y b⎠
2
10
2
× 51,150- + 126.2 ⎛ 13.1 + -----------7.75 -⎞
M cr = 0.474
----------------------------------⎝
15.61⎠
15.61
× 2.13 × 10 - + 563,310 ⎛ 333 + ---------197-⎞
M cr = 3.67
-----------------------------------------⎝
397 ⎠
397
Mcr = 3695 k-in. = 308 k-ft
> Ms = 288 k-ft
Mcr = 439,950,000 N-mm = 440 kN-mm
> Ms = 391.3 kN-m
∴ the strengthened section is uncracked at service.
∴ the strengthened section is uncracked at service.
Step 15—Check stress in prestressing steel
at service condition
Calculate the cracking moment and compare
to service moment:
2
Ms e
Pe ⎛
e
ε ps, s = ε pe + ---------- 1 + ---2-⎞ + --------⎝
Ac Ec
r ⎠ Ec Ig
⎛
2⎞
852 × 3605 ⎝
7.75 ⎠
126.2
13.1
289 × 12 × 13.1
ε ps, s = 0.00589 + -------------------------- ⎜ 1 + ------------⎟ + -------------------------------------2
3605 × 51,150
⎛
2⎞
5.5 × 10 × 24,700 ⎝
197 ⎠
333
563,310
- ⎜ 1 + -----------⎟
ε ps, s = 0.00589 + -------------------------------------------5
2
6
391.3 × 10 × 333
+ ------------------------------------------------10
24,700 × 2.13 × 10
εps,s = 0.0063 ≤ 0.0086
εps,s = 0.0063 ≤ 0.0086
fps,s = 28,500(0.0063) = 180 ksi
fps,s = 1.96 × 105(0.0063) = 1238 N/mm2
Calculate the steel stress using Eq. (10-24a):
⎧ 28,500ε ps, s for ε ps, s ≤ 0.0086
⎪
fps,s = ⎨
0.04
- for ε ps, s > 0.0086
⎪ 270 – ------------------------ε
ps
,
s – 0.07
⎩
Check the service stress limits of Eq. (10-20):
fps,s ≤ 0.82fpy
fps,s = 180 ksi < 0.82(230) = 189 ksi
OK
fps,s = 1238 N/mm2 < 0.82(1586) = 1300 N/mm2
OK
fps,s ≤ 0.74fpu
fps,s = 180 ksi < 0.74(270) = 200 ksi
OK
fps,s = 1238 N/mm2 < 0.74(1860) = 1376 N/mm2
OK
Step 16—Check stress in concrete at service
condition
Calculate the cracking moment and compare
to service moment:
2
Ms yt
–P
e
ε c, s = ----------e- ⎛ 1 + ---2-⎞ – ---------⎠
Ec Ig
Ac Ec ⎝
r
fc,s = Ecεc,s
⎛
2⎞
5.5 × 10 × 24,700 ⎝
197 ⎠
13.1 ⎞ 289 × 12 × 9.39
– 26.2 - ⎛ 1 + -----------ε c, s = -------------------------⎜
⎟ – -------------------------------------2
852 × 3605 ⎝
7.75 ⎠ 3605 × 51,150
– 563,310
391.3 × 10 × 238
333 - – ------------------------------------------------- ⎜ 1 + ---------ε c, s = -------------------------------------------⎟
10
5
2
εc,s = 0.00016
εc,s = 0.00016
2
fc,s ≤ 0.45fc′
fc,s = 3,605,000 psi (0.00016) = 577 psi
0.45fc′ = 0.45(4000) = 1800 psi
fc,s = 577 psi < 0.45fc′ = 1800 psi OK
6
24,700 × 2.13 × 10
fc,s = 24,700 N/mm2 (0.00016) = 3.95 N/mm2
0.45fc′ = 0.45(27.6) = 12.42 N/mm2
fc,s = 3.95 N/mm2 < 0.45fc′ = 12.42 N/mm2 OK
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Procedure
440.2R-57
Calculation in inch-pound units
Calculation in SI metric units
E Ms yb
f f, s = ⎛ -----f ⎞ ----------– ε bi E f
⎝ E c⎠ I
5360 ksi 289 k-ft × 12 in./ft × 15.61 in.
f f, s = ⎛ --------------------⎞ ----------------------------------------------------------------------⎝ 3605 ksi⎠
4
51,150 in.
⎛ 37,700 N/mm 2 ⎞ 391.3 × 10 6 N/mm × 397 mm
f f, s = ⎜ ------------------------------------⎟ ---------------------------------------------------------------------10
4
⎝ 24,700 N/mm 2⎠
2.13 × 10 mm
Because the section is uncracked at service,
the gross moment of inertia of the section
must be used.
–0.00003 × 5360 ksi
– 0.00003 × 37,700 N/mm2
ff,s = 1.41 ksi
ff,s = 9.7 N/mm2
0.55ffu = 0.55(85) = 47 ksi
0.55ffu = 0.55(586) = 322 N/mm2
ff,s = 1.41 ksi < 0.55ffu = 47 ksi OK
ff,s = 9.7 N/mm2 < 0.55ffu = 322 N/mm2 OK
Step 17—Check service stresses in the
FRP reinforcement
The stress in the FRP at service condition
can be calculated using Eq. (10-29):
The calculated stress in FRP should be
checked against the limits in Table 10.1. For
carbon FRP:
ff,s ≤ 0.55ffu
In detailing the FRP reinforcement, the FRP should be terminated a minimum of ldf , calculated per Eq. (13-2), past the point
on the moment diagram that represents cracking. The factored shear force at the termination should also be checked against the
shear force that causes FRP end peeling, estimated as 2/3 of the concrete shear strength. If the shear force is greater than 2/3 of
the concrete shear strength, FRP strips should be extended further toward the supports. U-wraps may also be used to reinforce
against cover delamination.
15.6—Shear strengthening of an interior T-beam
A reinforced concrete T-beam (fc′ = 3000 psi = 20.7 N/mm2) located inside of an office building is subjected to an increase
in its live-load-carrying requirements. An analysis of the existing beam indicates that the beam is still satisfactory for flexural
strength; however, its shear strength is inadequate to carry the increased live load. Based on the analysis, the nominal shear
strength provided by the concrete is Vc = 44.2 kips = 196.6 kN, and the nominal shear strength provided by steel shear
reinforcement is Vs = 19.6 kips = 87.2 kN. Thus, the design shear strength of the existing beam is φVn,existing = 0.75(44.2 kips
+ 19.6 kips) = 47.85 kips = 213 kN. The factored required shear strength, including the increased live load, at a distance d away
from the support is Vu = 57 kips = 253.5 kN. Figure 15.4 shows the shear diagram with the locations where shear strengthening
is required along the length of the beam.
Supplemental FRP shear reinforcement is designed as shown in Fig. 15.5 and summarized in Table 15.7. Each FRP strip
consists of one ply (n = 1) of a flexible carbon sheet installed by wet layup. The FRP system manufacturer’s reported material
properties are shown in Table 15.8.
Table 15.7—Configuration of the supplemental
FRP shear reinforcement
Fig. 15.4—Shear diagram showing demand versus existing
strength. The FRP reinforcement should correct the deficiency
shown shaded.
Fig. 15.5—Configuration of the supplemental FRP shear
reinforcement.
d
22 in.
559 mm
dfv
16 in.
406 mm
Width of each sheet wf
10 in.
254 mm
Span between each sheet sf
12 in.
305 mm
FRP strip length
70 in.
1778 mm
Table 15.8—Manufacturer’s reported FRP system
properties
Thickness per ply tf
0.0065 in.
0.165 mm
Ultimate tensile strength ffu*
550,000 psi
3790 N/mm2
Rupture strain εfu*
0.017 in./in.
0.017 mm/mm
Modulus of elasticity Ef
33,000,000 psi
227,530 N/mm2
440.2R-58
ACI COMMITTEE REPORT
The design calculations used to arrive at this configuration follow.
Procedure
Step 1—Compute the design material
properties
Calculation in inch-pound units
Calculation in SI metric units
ffu = CE ffu*
ffu = (0.95)(550 ksi) = 522.5 ksi
ffu = (0.95)(3.79 kN/mm2) = 3.60 kN/mm2
εfu = CE εfu*
εfu = (0.95)(0.017) = 0.016
εfu = (0.95)(0.017) = 0.016
2500
Le = ----------------------------------------------------------------------------------- = 2.0 in.
0.58
6
[ ( 1 ) ( 0.0065 in. ) ( 33 × 10 psi ) ]
416
- = 50.8mm
Le = -------------------------------------------------------------------------------------------------------------0.58
The beam is located in an enclosed and
conditioned space and a CFRP material will
be used. Therefore, per Table 9.1, an environmental-reduction factor of 0.95 is suggested.
Step 2—Calculate the effective strain
level in the FRP shear reinforcement
The effective strain in FRP U-wraps should
be determined using the bond-reduction coefficient κv . This coefficient can be computed
using Eq. (11-7) through (11-10).
2500
Le = ---------------------0.58
( nt f E f )
f c′ ⎞
k1 = ⎛ ----------⎝ 4000⎠
2⁄3
psi⎞ 2 ⁄ 3
k1 = ⎛ 3000
-------------------= 0.825
⎝ 4000 ⎠
3
2
[ ( 1 ) ( 0.1651 mm ) ( 227.5 × 10 kN/mm ) ]
2 2⁄3
20.7 kN/mm ⎞
k1 = ⎛ -------------------------------⎝
⎠
254
= 0.825
d fv – L e⎞
k2 = ⎛ ---------------⎝ d fv ⎠
in. – 2.0 in.⎞
k2 = ⎛ 16
= 0.875
⎝ ---------------------------------⎠
16 in.
mm – 50.8 mm-⎞ = 0.875
k2 = ⎛ 406
---------------------------------------------⎝
⎠
406 mm
k1 k2 Le
κ v = -------------- ≤ 0.75
468ε fu
( 0.82 ) ( 0.875 ) ( 2 in. )
κ v = -------------------------------------------------- = 0.193 ≤ 0.75
468 ( 0.016 )
0.82 ) ( 0.875 ) ( 50.8 mm )- = 0.193 ≤ 0.75
κ v = (-----------------------------------------------------------11,910 ( 0.016 )
εfe = 0.193(0.016) = 0.0031 ≤ 0.004
εfe = 0.193(0.016) = 0.0031 ≤ 0.004
Afv = 2(1)(0.0065 in.)(10 in.) = 0.13 in.2
Afv = 2(1)(0.1651 mm)(254 mm) = 83.87 mm2
ffe = (0.0031)(33,000 ksi) = 102 ksi
ffe = (0.0031)(227.6 kN/mm2) = 0.703 kN/mm2
The effective strain can then be computed
using Eq. (11-6b) as follows:
εfe = κvεfu ≤ 0.004
Step 3—Calculate the contribution of
the FRP reinforcement to the shear
strength
The area of FRP shear reinforcement can be
computed as:
Afv = 2nt f wf
The effective stress in the FRP can be
computed from Hooke’s law.
ffe = εfeEf
The shear contribution of the FRP can be
then calculated from Eq. (11-3):
A fv f fe ( sin α + cos α )d fv
V f = -----------------------------------------------------sf
2
0.13 in. ) ( 102 ksi ) ( 1 ) ( 16 in. )V f = (-------------------------------------------------------------------------( 12 in. )
83.87 mm ) ( 0.703 kN/mm ) ( 1 ) ( 406 mm -)
V f = (-------------------------------------------------------------------------------------------------------( 304.8 mm )
Vf = 17.7 kips
Vf = 78.5 kN
φVn = 0.75[44.2 + 19.6 + (0.85)(17.7)]
φVn = 59 kips > Vu = 57 kips
φVn = 0.75[196.6 + 87.2 + (0.85)(78.5)]
φVn = 263 kN > Vu = 253.3 kN
∴ the strengthened section is capable of sustaining
the required shear strength.
∴ the strengthened section is capable of sustaining
the required shear strength.
2
2
Step 4—Calculate the shear strength of
the section
The design shear strength can be computed
from Eq. (11-2) with ψf = 0.85 for U-wraps.
φVn = φ(Vc + Vs + ψfVf )
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
440.2R-59
15.7—Shear strengthening of an exterior column
A 24 x 24 in. (610 x 610 mm) square column requires an additional 60 kips of shear strength (ΔVu = 60 kips). The column is
located in an unenclosed parking garage and experiences wide variation in temperature and climate. A method of strengthening
the column using FRP is sought.
An E-glass-based FRP complete wrap is selected to retrofit the column. The properties of the FRP system, as reported by the
manufacturer, are shown in Table 15.9. The design calculations to arrive at the number of complete wraps required follow.
Table 15.9—Manufacturer’s reported FRP system
properties*
*
Thickness per ply tf
0.051 in.
1.3 mm
Guaranteed ultimate tensile strength ffu*
80,000 psi
552 N/mm2
Guaranteed rupture strain εfu*
0.020 in./in. 0.020 mm/mm
Modulus of elasticity Ef
4,000,000 psi 27,600 N/mm2
The reported properties are laminate properties.
Procedure
Step 1—Compute the design material
properties
The column is located in an exterior environment
and a GFRP material will be used. Therefore,
per Table 9.1, an environmental reduction
factor of 0.65 is suggested.
Calculation in inch-pound units
Calculation in SI metric units
ffu =CE ffu*
ffu = (0.65)(80 ksi) = 52 ksi
ffu = (0.65)(552 N/mm2) = 358.5 N/mm2
εfu =CE εfu*
εfu = (0.65)(0.020) = 0.013
εfu = (0.65)(0.020) = 0.013
εfe = 0.004 ≤ 0.75(0.013) = 0.010
εfe = 0.004 ≤ 0.75(0.013) = 0.010
∴ use an effective strain of εfe = 0.004.
∴ use an effective strain of εfe = 0.004.
60 kips
Vf, reqd = -------------------------- = 74.3 kips
0.85 ( 0.95 )
266.9 kN- = 330.5 kN
Vf, reqd = ------------------------0.85 ( 0.95 )
Step 2—Calculate the effective strain level
in the FRP shear reinforcement
The effective strain in a complete FRP wrap
can be determined from Eq. (11-6a):
εfe = 0.004 ≤ 0.75εfu
Step 3—Determine the area of FRP
reinforcement required
The required shear contribution of the FRP
reinforcement can be computed based on the
increase in strength needed, the strength
reduction factor for shear, and a partialreduction factor ψf = 0.95 for completely
wrapped sections in shear.
ΔV u
Vf, reqd = ------------φ ( ψf )
The required area of FRP can be determined
by reorganizing Eq. (11-3). The required area
is left in terms of the spacing.
V f, reqd s f
Afv, reqd = --------------------------------------------------ε fe E f ( sin α + cos α )d f
( 330.5 kN )s f
( 74.3 kips )s f
- = 4.91sf
Afv, reqd = ---------------------------------------------------------------------- = 0.194sf Afv, reqd = ----------------------------------------------------------------------------------------2
( 0.004 ) ( 4000 ksi ) ( 1 ) ( 24 in. )
( 0.004 ) ( 27.6 kN/mm ) ( 1 ) ( 610 mm )
Step 4—Determine the number of plies
and strip width and spacing
The number of plies can be determined in
terms of the strip width and spacing as follows:
A f, reqd
n = ------------2t f w f
0.194s f
s
- = 1.90 -----f
n = ---------------------------------2 ( 0.051 in. )w f
wf
4.91s f
s
n = ------------------------------- = 1.90 -----f
2 ( 1.3 mm )w f
wf
∴ use two plies (n = 2) continuously along the height
of the column (sf = wf ).
∴ use two plies (n = 2) continuously along the height
of the column (sf = wf).
440.2R-60
ACI COMMITTEE REPORT
15.8—Strengthening of a noncircular concrete column for axial load increase
A 24 x 24 in. (610 x 610 mm) square column requires an additional 20% of axial load-carrying capacity. Concrete and steel
reinforcement material properties as well as details of the cross section of the column are shown in Table 15.10. The column is
located in an interior environment, and a CFRP material will be used. A method of strengthening the column is sought.
Table 15.10—Column cross section details and material properties
fc′
6.5 ksi
45 MPa
fy
60 ksi
400 MPa
25 mm
rc
1 in.
Bars
12 No. 10
Ag
576 in.
2
3716 cm2
Ast
15.24 in.2
98 cm2
12φ32
ρg, %
2.65
2.65
φPn without FRP
2087 kip
9281 kN
φPn(req)
2504 kip
11,138 kN
Note: The column features steel ties for transverse reinforcement.
A carbon-based FRP complete wrap is selected to retrofit the columns. The properties of the FRP system, as reported by the
manufacturer, are shown in Table 15.11. The design calculations to arrive at the number of required complete wraps follow.
Table 15.11—Manufacturer’s reported FRP system
properties
Thickness per ply tf
0.013 in.
0.33 mm
Ultimate tensile strength ffu*
550 ksi
3792 MPa
Rupture strain εfu*
Modulus of elasticity Ef
Procedure
Step 1—Compute the design FRP material
properties
The column is located in an interior environment
and a CFRP material will be used. Therefore,
per Table 9.1, an environmental reduction
factor of 0.95 is suggested.
0.0167 in./in. 0.0167 mm/mm
33,000 ksi
227,527 MPa
Calculation in inch-pound units
Calculation in SI metric units
ffu =CE ffu*
ffu = (0.95)(550 ksi) = 522.5 ksi
ffu = (0.95)(3792 MPa) = 3603 MPa
εfu =CE εfu*
εfu = (0.95)(0.0167) = 0.0159 in./in.
εfu = (0.95)(0.0167) = 0.0159 mm/mm
1
f cc′ = -------------------------------------------------------------------- ×
2
2
0.85 × ( 576 in. – 15.24 in. )
1
f cc′ = ------------------------------------------------------------------------------------- ×
2
2
0.85 × ( 371,612 mm – 9832 mm )
2
2504 kip
⎛ -------------------------- – 60 ksi × 15.24 in. ⎞
⎝ 0.80 × 0.65
⎠
2
11,138 kN
⎛ -------------------------- – 414 MPa × 9832 mm ⎞
⎝ 0.80 × 0.65
⎠
fcc′ = 8.18 ksi
fcc′ = 56.4 MPa
Step 2—Determine the required maximum
compressive strength of confined concrete fcc′
fcc′ can be obtained by reordering Eq. (12-1):
φP n, req
1
f cc′ = --------------------------------– f y A st⎞
- ⎛ ---------------⎠
0.85 ( A g – A st ) ⎝ 0.80φ
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Procedure
440.2R-61
Calculation in inch-pound units
Calculation in SI metric units
8.18 ksi – 6.5 ksi
f l = ----------------------------------------- = 1.2 ksi
3.3 × 0.425
56.4 MPa – 44.8 MPa
f l = ----------------------------------------------------- = 8.3 MPa
3.3 × 0.425
2
A
κ a = -----e ⎛ b---⎞
A c ⎝ h⎠
κa = 0.425(1)2 = 0.425
κa = 0.425(1)2 = 0.425
⎛ b---⎞ ( h – 2r ) 2 + ⎛ h---⎞ ( b – 2r ) 2
c
c
⎝ b⎠
⎝ h⎠
1 – ----------------------------------------------------------------------------- – ρ g
Ae
3A g
----- = ------------------------------------------------------------------------------------------------1 – ρg
Ac
[ 2 × ( 1 ) ( 24 in. – 2 × 1 in. ) ]
1 – -------------------------------------------------------------------- – 0.0265
2
Ae
3 × 576 in.
----- = ---------------------------------------------------------------------------------------------------Ac
1 – 0.0265
[ 2 × ( 1 ) ( 610 mm – 2 × 25 mm ) ]
1 – -------------------------------------------------------------------------------- – 0.0265
2
Ae
3 × 371, 612 mm
----- = ---------------------------------------------------------------------------------------------------------------Ac
1 – 0.0265
Ae
----- = 0.425
Ac
Ae
----- = 0.425
Ac
Step 3—Determine the maximum confining
pressure due to the FRP jacket, fl
fl can be obtained by reordering Eq. (12-3):
f cc′ – f c′
f l = -----------------3.3κ a
where
2
2
Step 4—Determine the number of plies n
n can be obtained by reordering Eq. (12-4):
2
2
fl b + h
n = ----------------------ψ f 2E f t f ε fe
εfe = κε εfu
2
2
2
2
1.2 ksi ( 24 in. ) + ( 24 in. )
n = --------------------------------------------------------------------------------------------------------------------------------–3
0.95 × 2 × 33,000 ksi × 0.013 in. × ( 8.8 × 10 in./in. )
8.3 MPa (610 mm) + (610 mm)
n = ----------------------------------------------------------------------------------------------------------------------------------------------–3
0.95 × 2 × 227,527 MPa × 0.33 mm × ( 8.8 × 10 mm/mm )
n = 5.7 ≈ 6 plies
n = 5.7 ≈ 6 plies
εfe = 0.55 × 0.0159 in./in. = 8.8 × 10–3 in./in.
εfe = 0.55 × 0.0159 mm/mm = 8.8 × 10–3 mm/mm
f
1.2 ksi
----l- = ---------------- = 0.18 > 0.08 OK
f c′
6.5 ksi
f
8.3 MPa
----l- = ----------------------- = 0.18 > 0.08 OK
f c′
44.8 MPa
ε cc = ( 0.002 in./in. ) ⎛ 1.5 + 12 × 0.425 ×
⎝
ε cc = ( 0.002 mm/mm ) ⎛ 1.5 + 12 × 0.425 ×
⎝
Checking the minimum confinement ratio:
f
----l- ≥ 0.08
f c′
Step 5—Verify that the ultimate axial
strain of the confined concrete εccu ≤ 0.01
εccu can be obtained using Eq. (12-6):
f ε 0.45
ε ccu = ε c′ ⎛ 1.5 + 12κ b ----l- ⎛ -----fe-⎞ ⎞
⎝
f c′ ⎝ ε c′ ⎠ ⎠
–3
1.2
ksi- ⎛ --------------------------------------8.8 × 10 in./in.⎞
--------------6.5 ksi ⎝ 0.002 in./in. ⎠
where
0.5
A
κ b = -----e ⎛ h---⎞
⎝
⎠
Ac b
If the case that εccu was to be greater than
0.01, then fcc′ should be recalculated from the
stress-strain model using Eq. (12-2).
0.45
⎞
⎠
–3
8.3 MPa- ⎛ --------------------------------------------8.8 × 10 mm/mm-⎞
---------------------44.8 MPa ⎝ 0.002 mm/mm ⎠
0.45
εcc = 0.0067 in./in. < 0.01 OK
εcc = 0.0067 mm/mm < 0.01 OK
κb = 0.425(1)0.5 = 0.425
κb = 0.425(1)0.5 = 0.425
⎞
⎠
440.2R-62
ACI COMMITTEE REPORT
15.9—Strengthening of a noncircular concrete column for increase in axial and bending forces
The column in Example 15.6 is subjected to an ultimate axial compressive load Pu = 1900 kip (8451 kN) and an ultimate
bending moment Mu = 380 kip-ft (515 kN-m) (e = 0.1h). It is sought to increase load demands by 30% at constant eccentricity
(Pu = 2470 kip, Mu = 494 kip-ft). Note: 1 kN/mm2 = 1000 MPa or 1 MPa = 10–3 kN/mm2.
Procedure
Calculation in inch-pound units
Calculation in SI metric units
Step 1—Determine the simplified curve for
the unstrengthened column (n = 0 plies)
Points A, B, and C can be obtained by wellknown procedures, and also by using Eq. (D-1)
to (D-5) considering ψf = 1; fcc′ = fc′; E2 = 0;
and εccu = εcu = 0.003.
φPn(A) = 2087 kip; φMn(A) = 0 kip-ft
φPn(A) = 9283 kN; φMn(A) = 0 kN-m
φPn(B) = 1858 kip; φMn(B) = 644 kip-ft
φPn(B) = 8265 kN; φMn(B) = 873 kN-m
φPn(C) = 928 kip; φMn(C) = 884 kip-ft
φPn(C) = 4128 kN; φMn(C) = 1199 kN-m
Step 2—Determine the simplified curve for
a strengthened column
A wrapping system composed of six plies will
be the starting point to construct the bilinear
Curve A-B-C and then be compared with the
position of the required Pu and Mu.
Points A, B, and C of the curve can be
computed using Eq. (12-1), (D-1), and (D-2): Point A:
Nominal axial capacity:
φPn(A) = φ0.8(0.85fcc′ (Ag – Ast) + fy Ast)
φPn(A) = 0.65 × 0.8(0.85 × 8.26 ksi × (576 in.2 –
φPn(B,C) = φ(A(yt )3 + B(yt )2 + C(yt )
15.24 in.2) + 60 ksi + 15.24 in.2
+ D) + ΣAsi fsi]
φPn(A) = 2523 kip
4
3
φMn(B,C) = φ(E(yt ) + F(yt ) + G(yt )
+ H(yt ) + I) + ΣAsi fsidi
Point A:
Nominal axial capacity:
φPn(A) = 0.65 × 0.8(0.85 × 56.96 MPa × (371,612 mm2
– 9832 mm2) + 414 MPa + 9232 mm2
φPn(A) = 11,223 kN
2
where
fcc′ = 6.5 ksi + 3.3(0.425)(1.26 ksi)
fcc′ = 8.26 ksi
where
fcc′ = 44.8 MPa + 3.3(0.425)(8.7 MPa)
fcc′ = 56.96 MPa
(24 in.) + ( 24 in. )
(610 mm) + ( 610 mm )
The coefficients A, B, C, D, E, F, G, H, and I
mm
in.
of the previous expressions are given by
0.95 × 2 × 227,500 MPa × 6 × 0.33 mm × ⎛ 0.55 × 0.0159 ---------⎞
0.95 × 2 × 33,000 ksi × 6 × 0.013 in. × ⎛ 0.55 × 0.0159 ------⎞
⎝
⎝
mm⎠
in.⎠
Eq. (D-3):
f l = ------------------------------------------------------------------------------------------------------------------------------------------- f l = -----------------------------------------------------------------------------------------------------------------------------------------------------2
2
2
2
2
– b ( E c – E 2 ) ⎛ ε ccu⎞ 2
-------A = -----------------------------⎝ c ⎠
12f c′
b ( E c – E 2 ) ⎛ ε ccu⎞
- -------B = -----------------------⎝ c ⎠
2
C = bfc′
bcE
D = bfc′ + ------------2 ( ε ccu )
2
2
– b ( E c – E 2 ) ⎛ ε ccu⎞ 2
-------E = -----------------------------⎝ c ⎠
16f c′
( E c – E 2 ) ⎛ ε ccu⎞ 2 b ( E c – E 2 ) ⎛ ε ccu⎞
- --------- + -------------------------- --------F = b ⎛ c – h---⎞ -----------------------⎝ c ⎠
⎝
3
2⎠ 12f c′ ⎝ c ⎠
2
( E c – E 2 ) ⎛ ε ccu⎞ ⎞
G = – ⎛ b--- f c′ + b ⎛ c – h---⎞ --------------------- ⎝ ---------⎠
⎝
⎝2
c ⎠
2
2⎠
h
H = bf c′ ⎛ c – ---⎞
⎝
2⎠
2
2
bc
h bc E
I = -------- f c′ – bcf c′ ⎛ c – ---⎞ +--------------2- ( ε ccu )
⎝
2
3
2⎠
bcE
– -----------2- ⎛ c – h---⎞ ( ε ccu )
2 ⎝
2⎠
fl = 1.26 ksi
fl = 8.67 MPa
Point B:
Nominal axial capacity:
Point B:
Nominal axial capacity:
φPn(B) = 0.65[–0.22 kip/in.3(15.33 in.)3 + 10.17 ksi φPn(B) = 0.65[–6.003 × 10–5 kN/mm3(389 mm)3 + 70.14
(15.33 in.)2 – 56 kip/in.(15.33 in.) + 3645.2 kips] × 10–3 kN/mm2(389 mm)2 – 27.32 kN/mm(389 mm) +
+ 5.08 in.2 (60 ksi) + 2.54 in.2(60 ksi) + 2.54 in.2 16,215 kN] + 3277 mm2(414 MPa) + 1639 mm2(414 MPa)
(37.21 ksi)]
+ 1639 mm2(257 ksi)
φPn(B) = 2210 kip
where
φPn(B) = 9892 kN
where
2
2
2
24 in.(4595 ksi – 190.7 ksi) ⎛ 0.0042 in./in.⎞
610 mm (31,685 MPa – 1315 MPa) ⎛ 0.0042 mm/mm⎞ 2
A = –------------------------------------------------------------------------------------------------------- A = –------------------------------------------------------------------------------------------- -------------------------------------⎝
⎠
⎝
⎠
12 × 6.5 ksi
22 in.
12 × 44.8 MPa
559 mm
= –0.22 kip/in.3
= –6.003 × 10–5 kN/mm3
in.(4595 ksi – 190.7 ksi)- ⎛ 0.0042
in./in.-⎞
B = 24
----------------------------------------------------------------------------------------------⎝
⎠
2
22 in.
mm(31,685 MPa – 1315 MPa) 0.0042 mm/mm
------------------------------------------------------------------------------------ ⎛ --------------------------------------⎞
B = 600
⎝
⎠
= 10.17 ksi
= 70.14 × 10–3 kN/mm2
C = –24 in. × 6.5 ksi = –156 kip/in.
C = –610 mm × 44.84 MPa = –27.32 kN/mm
D = 24 in. × 22 in. × 6.5 ksi
D = 610 mm × 559 mm × 44.8 MPa
24 in. × 22 in. × 190.7 ksi
+ -------------------------------------------------------------- (0.0042 in./in.)
2
610 mm × 559 mm × 1315 MPa
+ ------------------------------------------------------------------------------ (0.0042 mm/mm)
2
D = 3645.2 kip
D = 16,215 kN
2
559 mm
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Procedure
Calculation in inch-pound units
Step 2—(cont.)
Key parameters of the stress-strain model:
440.2R-63
Calculation in SI metric units
For the calculation of the coefficients, it is necessary For the calculation of the coefficients, it is necessary to
compute key parameters from the stress-strain
to compute key parameters from the stress-strain
model:
model:
ε t′
y t = c ------ε ccu
0.003 in./in.- = 15.33 in.
y t = 22 in. × ------------------------------0.0042 in./in.
0.003 mm/mm- = 389 mm
y t = 559 mm × ------------------------------------0.0042 mm/mm
⎧d
for Point B
⎪
c = ⎨
ε ccu
- for Point C
⎪ d ε-------------------⎩ sy + ε ccu
c = 22 in.
c = 559 mm
2f c′
ε t′ = ---------------Ec – E2
2 × 6.5 ksi
ε t′ = ----------------------------------------------- = 0.003 in./in.
4595 ksi – 190.7 ksi
2 × 44.8 MPa
ε t′ = ----------------------------------------------------------- = 0.003 mm/mm
31,685 MPa – 1315 MPa
f cc′ – f c′
E 2 = -----------------ε ccu
7.31 ksi – 6.5 ksi
E 2 = ----------------------------------------- = 190.7 ksi
0.0042 in./in.
50.4 MPa – 44.8 MPa
E 2 = ---------------------------------------------------- = 1315 MPa
0.0042 mm/mm
fcc′ = fc′ + 3.3κa fl
fcc′ = 6.5 ksi + 3.3(0.425)(0.58 ksi) = 7.31 ksi
fcc′ = 44.8 MPa + 3.3(0.425)(3.97 MPa) = 50.4 MPa
f ε 0.45
ε ccu = ε c′ ⎛ 1.5 + 12κ b ----l- ⎛ -----fe-⎞ ⎞
⎝
f c′ ⎝ ε c′ ⎠ ⎠
0.58 ksi 0.004 in./in.
ε ccu = 0.002 in./in. ⎛ 1.5 + 12 × 0.425 ⎛ -------------------⎞ ⎛ -----------------------------⎞
⎝
⎝ 6.5 ksi ⎠ ⎝ 0.002 in./in.⎠
mm/mm-⎞
MPa-⎞ ⎛ 0.004
⎞ ε ccu = 0.002 mm/mm ⎛⎝ 1.5 + 12 × 0.425 ⎛⎝ 3.97
------------------------------------------------------44.8 MPa⎠ ⎝ 0.002 mm/mm⎠
⎠
0.45
0.45
⎞
⎠
εccu = 0.0042 in./in.
εccu = 0.0042 mm/mm
κa = κb = 0.425
κa = κb = 0.425
0.95 × 2 × 33,000 ksi × 6 × 0.013 in. × (0.004 in./in.)
f l = ------------------------------------------------------------------------------------------------------------------------------2
2
(24 in.) + ( 24 in. )
0.95 × 2 × 227,527 MPa × 6 × 0.33 mm × (0.004 mm/mm)
f l = --------------------------------------------------------------------------------------------------------------------------------------------2
2
(610 mm) + ( 610 mm )
ε fe = min ( 0.004, κ ε ε fu )
2
A
κ a = -----e ⎛ b---⎞
⎝
⎠
Ac h
A
κ b = -----e ⎛ h---⎞
A c ⎝ b⎠
0.5
ψ f 2E f nt f ε fe
f l = -------------------------2
2
b +h
Notes: The designer should bear in mind that,
for the case of pure compression, the effective Checking the minimum confinement ratio:
Checking the minimum confinement ratio:
strain in the FRP, εfe , is limited by κεεfu and,
in the case of combined axial and bending, by
fl /fc′ = 0.58 ksi/6.5 ksi = 0.09 ≥ 0.08 OK
fl /fc′ = 3.97 MPa/44.8 MPa = 0.09 ≥ 0.08 OK
εfe = min(0.004, κεεfu).
The strains in each layer of steel are determined by The strains in each layer of steel are determined by
similar triangles in the strain distribution. The corre- similar triangles in the strain distribution. The corresponding stresses are then given by:
sponding stresses are then given by:
fs1 = εs1Es = 0.0038 in./in. × 29,000 ksi → 60 ksi fs1 = εs1Es = 0.0038 mm/mm × 200,000 MPa → 414 MPa
fs2 = εs2Es = 0.0026 in./in. × 29,000 ksi → 60 ksi fs2 = εs2Es = 0.0026 mm/mm × 200,000 MPa → 414 MPa
fs3 = εs3Es = 0.0013 in./in. × 29,000 ksi = 37.2 ksi fs3 = εs3Es = 0.0013 mm/mm × 200,000 MPa = 257 MPa
fs4 = εs4Es = 0 in./in. × 29,000 ksi = 0 ksi
fs4 = εs4Es = 0 mm/mm × 200,000 MPa = 0 MPa
Nominal bending moment:
Nominal bending moment:
φMn(B) = 0.65[–0.166 kip/in.3(15.33 in.)4 + 8.99 ksi
φMn(B) = 0.65[–4.502 × 10–5 kN/mm3(389 mm)4 +
(15.33 in.)3 – 179.73 kip/in.(15.33 in.)2 + 1560 kip 62.01 × 10–3 kN/mm3(389 mm)3 – 31.48 kN/mm(389
(15.33 in.) + 4427 kip-in.] + 5.08 in.2(60 ksi)(10 in.) mm)2 + 6939 kN(389 mm) + 500,162 kN-mm] + 3277
+ 2.54 in.2(60 ksi)(3.3 in.) – 2.54 in.2(37.21 ksi)(3.3 in.) mm2(414 MPa)(254 mm) + 1639 mm2(414 MPa)(85 mm)
– 1639 mm2(257 MPa)(85 mm)
φMn(B) = 924 kN-m
φMn(B) = 682 kip-ft
where
where
2
2
610 mm(31,685 MPa – 1315 MPa) - ⎛ 0.0042
mm/mm-⎞ 2
in./in.-⎞ 2 E = –-----------------------------------------------------------------------------------------24 in.(4595 ksi – 190.7 ksi) ⎛ 0.0042
------------------------------------------------------------------E = –-----------------------------------------------------------------------⎝
⎠
16 × 44.8 MPa
559 mm
⎝
⎠
16 × 6.5 ksi
22 in.
= –0.166 kip/in.3
= –0.4502 × 10–5 kN/mm3
2
2
(31,685 MPa – 1315 MPa)
ksi – 190.7 ksi)- F = 610 mm(559 mm – 305 mm) × -----------------------------------------------------------------F = 24 in.(22 in. – 12 in.) × (4595
----------------------------------------------------12 × 44.8 MPa
12 × 6.5 ksi
2
0.0042
mm/mm
610
mm(31,685
MPa
– 1315 MPa)
⎛
⎞
-------------------------------------- + ------------------------------------------------------------------------------------ ×
in./in.-⎞ 2 + 24
in.(4595 ksi – 190.7 ksi)⎝
⎠
⎛ 0.0042
559 mm
3
----------------------------------------------------------------------------------------------×
⎝
⎠
22 in.
3
mm/mm
⎛ 0.0042
--------------------------------------⎞ = 62.01 × 10–3 kN/mm2
⎝
⎠
559 mm
in./in.⎞
⎛ 0.0042
-------------------------------- = 8.99 ksi
⎝
⎠
22 in.
440.2R-64
ACI COMMITTEE REPORT
Procedure
Step 2—(cont.)
Calculation in inch-pound units
Calculation in SI metric units
G = 6.5 ksi × 12 in. + 24 in.(22 in. – 12 in.)
4595 ksi – 190.7 ksi
in./in.-⎞
× ⎛ ------------------------------------------------⎞ ⎛ 0.0042
------------------------------⎝
⎠⎝
⎠
2
22 in.
G = 44.8 MPa × 305 mm + 610 mm(559 mm – 305 mm)
31,685 MPa – 1315 MPa
mm/mm-⎞
× ⎛ ------------------------------------------------------------⎞ ⎛ 0.0042
------------------------------------⎝
⎠⎝
⎠
2
559 mm
G = –179.73 kip/in.
G = –31.48 kN/mm
H = 6.5 ksi × 24 in.(22 in. – 12 in.) = 1560 kip
H = 44.8 MPa × 610 mm(559 mm – 305 mm) = 6939 kN
2
2
( 22 in. )
( 559 mm )
I = 6.5 ksi × 24 in. × -------------------- – 6.5 ksi(22 in. – 12 in.) I = 44.8 MPa × 610 mm × -------------------------- – 44.8 MPa
2
2
(559 mm – 305 mm) × (559 mm)(610 mm) + 1315 MPa
× 22 in. × 24 in. + 190.7 ksi × 24 in. ×
2
2
( 22 in. )
( 559 mm )
-------------------- (0.0042 in./in.) – 190.7 ksi × 24 in. ×
× 610 mm × -------------------------- (0.0042 mm/mm) – 1315 MPa ×
3
3
22 in.
559
mm
------------- (22 in. – 12 in.)(0.0042 in./in.
610 mm × ------------------- (559 mm – 305 mm)(0.0042 mm/mm)
3
2
= 4427 kip-in.
= 500,162 kN-mm
The distances from each layer of steel reinforcement The distances from each layer of steel reinforcement to
to the geometric centroid of the cross section are:
the geometric centroid of the cross section are:
d1 = 10 in.
d1 = 254 mm
d2 = d3 = 3.3 in.
d2 = d3 = 85 mm
Point C:
Point C:
Nominal axial capacity:
Nominal axial capacity:
φPn(C) = 0.65[–0.49 kip/in.3(10.3 in.)3 + 15.14 ksi φPn(C) = 0.65[–1.33 ×10–4 kN/mm3(262 mm)3 + 104.41
(10.3 in.)2 – 156 kip-in.(10.3 in.) + 2448.71 kips] × 10–3 kN/mm2 × (262 mm)2 – 27.32 kN/mm(262 mm)
+ 5.08 in.2(60 ksi) + 2.54 in.2(50.79 ksi) + 2.54 in.2 + 10,892 kN] + 3277 mm2(414 MPa) + 1315 mm2(350
(–4.61 ksi) + 5.08 in.2(–60 ksi)
MPa) + 1315 mm2 (–31.8 MPa) + 3277 mm2(–414 MPa)
φPn(C) = 1320 kip
φPn(C) = 5870 kN
where
where
2
2
– 610 mm(31,681 MPa – 1315 MPa) 2 0.0042 mm/mm 2
–
24
in.(4595
ksi
–
190.7
ksi)
0.0042
in./in.
⎛
⎞
A = ---------------------------------------------------------------------- -------------------------------- A = ----------------------------------------------------------------------------------------- ⎛⎝ --------------------------------------⎞⎠
12 × 44.8 MPa
375 mm
⎝ 14.78 in. ⎠
12 × 6.5 ksi
= –0.49 kip/in.3
= –1.33 × 10–4 kN/mm3
24 in.(4595 ksi – 190.7 ksi)- ⎛ 0.0042
in./in.-⎞
B = –--------------------------------------------------------------------------------------------------⎝ 14.78 in. ⎠
2
– 610 mm(31,681 MPa – 1315 MPa)- ⎛ ------------------------------------0.0042 mm/mm-⎞
B = ---------------------------------------------------------------------------------------⎝
⎠
2
–3
kN/mm
375 mm
2
= 15.14 ksi
= –104.41 × 10
C = –24 in. × 6.5 ksi = –156 kip/in.
C = –610 mm × 44.8 MPa = –27.32 kN/mm
D = 24 in. × 14.78 in. × 6.5 ksi
D = 610 mm × 375 mm × 44.8 MPa
24 in. × 14.78 in. × 190.7 ksi
+ --------------------------------------------------------------------- × (0.0042 in./in.)
2
610 mm × 375 mm × 1315 MPa
+ ----------------------------------------------------------------------------- × (0.0042 mm/mm)
2
= 2448.71 kip
= 10,892 kN
For the calculation of the coefficients, it is necessary For the calculation of the coefficients, it is necessary to
compute key parameters from the stress-strain
to compute key parameters from the stress-strain
model:
model:
0.003 in./in.- = 10.3 in.
y t = 14.78 in. ------------------------------0.0042 in./in.
0.003 mm/mm- = 262 mm
y t = 375 mm ------------------------------------0.0042 mm/mm
0.0042 in./in.
0.0042 mm/mm
c = 22 in. ⎛ ----------------------------------------------------------------------⎞ = 14.78 in. c = 560 mm ( ---------------------------------------------------------------------------------- ) = 375 mm
⎝ 0.0021 in./in. + 0.0042 in./in.⎠
0.0021 mm/mm + 0.0042 mm/mm
The strains in each layer of steel are determined by The strains in each layer of steel are determined by
similar triangles in the strain distribution. The corre- similar triangles in the strain distribution. The corresponding stresses are then given by:
sponding stresses are then given by:
fs1 = εs1Es = 0.0037 in./in. × 29,000 ksi → 60 ksi fs1 = εs1Es = 0.0037 mm/mm × 200,000 MPa → 414 MPa
fs2 = εs2Es = 0.0018 in./in. × 29,000 ksi = 50.78 ksi fs2 = εs2Es = 0.0018 mm/mm × 200,000 MPa = 350 MPa
–4
fs3 = εs3Es = –1.59 × 10–4 in./in. × 29,000 ksi = –4.61 ksi fs3 = εs3Es = –1.59 × 10 mm/mm × 200,000 MPa = –31.8 MPa
fs4 = εs4Es = –0.0021 in./in. × 29,000 ksi = –60 ksi fs4 = εs4Es = –0.0021 mm/mm × 200,000 MPa = –414 MPa
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Procedure
Step 2—(cont.)
Calculation in inch-pound units
440.2R-65
Calculation in SI metric units
Nominal bending moment:
Nominal bending moment:
φMn(C) = 0.65[–0.37 kip/in.3(10.3 in.)4 + 11.46 ksi φMn(C) = 0.65[–9.98 × 10–5 kN/mm3(262 mm)4 + 79 ×
(10.3 in.)3 – 120.08 kip/in.(10.3 in.)2 + 433.5 kip
10–3 kN/mm2(262 mm)3 – 21.03 kN/mm(262 mm)2 +
1928 kN(262 mm) + 1,315,453 kN-mm] + 3277
(10.3 in.) + 11,643 kip-in.] + 5.08 in.2(60 ksi)(10 in.)
2
2
+ 2.54 in.2(50.79 ksi)(3.33 in.) – 2.54 in.2(–4.61 ksi) mm (414 MPa)(254 mm) + 1639 mm (–31.8 MPa)(85
2
2
(–414
MPa)
(254
mm)
mm)
–
3277
mm
(3.33 in.) – 5.08 in. (–60 ksi)(10 in.)
φMn(C) = 1345 kN-m
φMn(C) = 992 kip-ft
where
where
2
2
610 mm(31,681 MPa – 1315 MPa) ⎛ 0.0042 mm/mm⎞ 2
24 in.(4595 ksi – 190.7 ksi) ⎛ 0.0042 in./in.⎞ 2 E = –------------------------------------------------------------------------------------------ -------------------------------------E = –-----------------------------------------------------------------------------------------------------⎝
⎠
16
×
44.8
MPa
375 mm
⎝ 14.78 in. ⎠
16 × 6.5 ksi
= –9.98 × 10–5 kN/mm3
= –0.37 kip/in.3
2
2
(31,681 MPa – 1315 MPa)
ksi – 190.7 ksi)- F = 610 mm(375 mm – 305 mm) × ----------------------------------------------------------------F = 24 in.(14.78 in. – 12 in.) (4595
----------------------------------------------------12 × 44.8 MPa
12 × 6.5 ksi
2
mm/mm-⎞ + 610
mm(31,681 MPa – 1315 MPa)- ×
⎛ 0.0042
----------------------------------------------------------------------------------------------------------------------in./in. 2 24 in.(4595 ksi – 190.7 ksi)
⎛ 0.0042
⎝
--------------------------------⎞ + -----------------------------------------------------------------375 mm ⎠
3
⎝ 14.78 in. ⎠
3
0.0042 mm/mm⎞
–3
⎛
-------------------------------------- = 79 × 10 kN/mm2
in./in.-⎞
⎛ 0.0042
⎝
------------------------------= 11.46 ksi
375 mm ⎠
⎝ 14.78 in. ⎠
G = –6.5 ksi × 12 in. + 24 in.(14.78 in. – 12 in.)
4595 ksi – 190.7 ksi 0.0042 in./in.
× ⎛ ------------------------------------------------⎞ ⎛ --------------------------------⎞
⎝
⎠ ⎝ 14.78 in. ⎠
2
G = –120.08 kip/in.
G = –44.8 MPa × 305 mm + 610 mm(375 mm – 305 mm)
31,681 MPa – 1315 MPa 0.0042 mm/mm
× ⎛ ------------------------------------------------------------⎞ ⎛ --------------------------------------⎞
⎝
⎠⎝
375 mm ⎠
2
G = –21.03 kN/mm
H = 6.5 ksi × 24 in.(14.78 in. – 12 in.) = 433.5 kip
H = 44.8 MPa × 610 mm(375 mm – 305 mm) = 1928 kN
2
( 14.78 in. )- – 6.5 ksi(14.78 in. –
2
I = 6.5 ksi × 24 in. × --------------------------( 375 mm )
2
I = 44.8 MPa × 610 mm × --------------------------- – 44.8 MPa
2
12 in.)(14.78 in.)(24 in.) + 190.7 ksi × 24 in. ×
(375 mm – 305 mm) × (375 mm)(610 mm) + 1315 MPa
2
( 14.78 in. )2
--------------------------(0.0042 in./in.) – 190.7 ksi × 24 in. ×
( 375 mm )
3
× 610 mm × --------------------------- (0.0042 mm/mm) – 1315 MPa ×
3
14.78
in.-------------------(14.78 in. – 12 in.)(0.0042 in./in.)
375 mm
2
610 mm × -------------------- (375 mm – 305 mm)(0.0042 mm/mm)
= 11,643 kip-in.
2
= 1,315,453 kN-mm
Step 3—Comparison of simplified partial The following table summarizes the axial and bending The following table summarizes the axial and bending
interaction diagram with required Pu and nominal capacities (unstrengthened and strengthened) nominal capacities (unstrengthened and strengthened)
for Points A, B, and C. These points are plotted in the for Points A, B, and C. These points are plotted in the
Mu .
figure below.
figure below.
n = 0 plies
(unstrengthened
member)
Point
A
φPn, kip
2087
φMn,
kip-ft
0
B
C
1858
928
644
884
n = 0 plies
(unstrengthened
member)
n = 6 plies
φPn, kN
9283
11,223
φMn,
kN-m
0
8264
4128
873
1199
9829
5870
924
1345
φPn, kN
2523
Point
A
2210
1320
682
992
B
C
φPn, kip
n = 6 plies
φMn,
kN-m
0
φMn,
kip-ft
0
440.2R-66
ACI COMMITTEE REPORT
CHAPTER 16—REFERENCES
16.1—Referenced standards and reports
The standards and reports listed below were the latest
editions at the time this document was prepared. Because
these documents are revised frequently, the reader is advised
to contact the proper sponsoring group if it is desired to refer
to the latest version.
American Concrete Institute (ACI)
216R
Guide for Determining Fire Endurance of
Concrete Elements
224.1R
Causes, Evaluation, and Repair of Cracks in
Concrete Structures
318
Building Code Requirements for Structural
Concrete and Commentary
364.1R
Guide for Evaluation of Concrete Structures
before Rehabilitation
437R
Strength Evaluation of Existing Concrete Buildings
440R
Report on Fiber-Reinforced Polymer (FRP)
Reinforcement for Concrete Structures
440.3R
Test Methods for Fiber-Reinforced Polymers
(FRPs) for Reinforcing or Strengthening
Concrete Structures
503R
Use of Epoxy Compounds with Concrete
503.4
Standard Specification for Repairing Concrete
with Epoxy Mortars
546R
Concrete Repair Guide
American National Standards Institute (ANSI)
Z-129.1
Hazardous Industrial Chemicals Precautionary
Labeling
D3165
D3171
D3418
D3479/
D3479M
D3528
D3846
D4065
D4475
D4476
D4541
D4551
D5379/
D5379
D7205
E84
American Society of Civil Engineers (ASCE)
7-05
Minimum Design Loads for Buildings and Other
Structures
ASTM International
D648
Test Method for Deflection Temperature of
Plastics Under Flexural Load in the Edgewise
Position
D696
Test Method for Coefficient of Linear Thermal
Expansion of Plastics Between –30 °C and 30 °C
with a Vitreous Silica Dilatometer
D790
Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical
Insulating Materials
D2240
Test Method for Rubber Hardness—Durometer
Hardness
D2344/
Test Method for Short-Beam Strength of Polymer
D2344M Matrix Composite Materials and Their Laminates
D2538
Practice for Fusion of Poly Vinyl Chloride
(PVC) Compounds Using a Torque Rheometer
D2584
Test Method for Ignition Loss of Cured Reinforced
Resins
D2990
Test Method for Tensile, Compressive, and
Flexural Creep and Creep-Rupture of Plastics
D3039
Test Method for Tensile Properties of Polymer
Matrix Composite Materials
E119
E328
E831
E1356
E1640
E2092
Test Method for Strength Properties of Adhesives
in Shear by Tension Loading of Single-LapJoint Laminated Assemblies
Test Methods for Constituent Content of
Composite Materials
Test Method for Transition Temperatures and
Enthalpies of Fusion and Crystallization of
Polymers by Differential Scanning Calorimetry
Test Method for Tension-Tension Fatigue of
Polymer Matrix Composite Materials
Test Method for Strength Properties of Double
Lap Shear Adhesive Joints by Tension Loading
Test Method for In-Plane Shear Strength of
Reinforced Plastics
Practice for Plastics: Dynamic Mechanical Properties: Determination and Report of Procedures
Test Method for Apparent Horizontal Shear
Strength of Pultruded Reinforced Plastic Rods
by the Short-Beam Method
Test Method for Flexural Properties of Fiber
Reinforced Pultruded Plastic Rods
Test Method for Pull-Off Strength of Coatings
Using Portable Adhesion Testers
Standard Specification for Poly(Vinyl Chloride)
(PVC) Plastic Flexible Concealed WaterContainment Membrane
Test Method for Shear Properties of Composite
Materials by the V-Notched Beam Method
Test Method for Tensile Properties of Fiber
Reinforced Polymer Matrix Composite Bars
Test Method for Surface Burning Characteristics
of Building Materials
Test Methods for Fire Tests of Building
Construction and Materials
Test Methods for Stress Relaxation Tests for
Materials and Structures
Test Method for Linear Thermal Expansion of
Solid Materials by Thermomechanical Analysis
Test Method for Assignment of the Glass Transition Temperatures by Differential Scanning
Calorimetry
Test Method for Assignment of the Glass Transition Temperature by Dynamic Mechanical
Analysis
Test Method for Distortion Temperature in ThreePoint Bending by Thermomechanical Analysis
Canadian Standards Association (CSA)
CSA S806 Design and Construction of Building Components
with Fiber-Reinforced Polymers
CAN/
Canadian Highway Bridge Design Code
CSA-S6
China Association for Engineering Construction Standardization (CECS)
CECS-146 Technical Specification for Strengthening
Concrete Structures with Carbon Fiber Reinforced
Polymer Laminates
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
Code of Federal Regulations (CFR)
CFR 16, Hazardous Substances and Articles; Administration
Part 1500 and Enforcement Regulations
CFR 49, Subchapter C Transportation
International Conference of Building Officials (ICBO)(now
International Code Council)
AC125
Acceptance Criteria for Concrete and Reinforced
and Unreinforced Masonry Strengthening Using
Fiber-Reinforced Composite Systems
International Concrete Repair Institute (ICRI)
03730
Guide for Surface Preparation for the Repair of
Deteriorated Concrete Resulting from Reinforcing
Steel Corrosion
03732
Guideline for Selecting and Specifying Concrete
Surface Preparation for Sealers, Coatings, and
Polymer Overlays
03739
Guideline to Using In-Situ Tensile Pull-Off
Tests to Evaluate Bond of Concrete Surface
Materials
These publications may be obtained from these organizations:
American Concrete Institute (ACI)
P.O. Box 9094
Farmington Hills, MI 48333-9094
www.concrete.org
American National Standards Institute (ANSI)
11 West 42nd Street
New York, NY 10036
www.ansi.org
American Society of Civil Engineers (ASCE)
1801 Alexander Bell Drive
Reston, VA 20191-4400
www.asce.org
ASTM International
100 Barr Harbor Drive
West Conshohocken, PA 19428
www.astm.org
Canadian Standards Association (CSA)
178 Rexdale Blvd.
Toronto, ON
M9W 1R3 Canada
www.csa.ca
China Association for Engineering Construction
Standardization (CECS)
No. 12 Chegongzhuang St.
Xicheng District
Beijing 100044
China
440.2R-67
Code of Federal Regulations (CFR)
Government Printing Office
732 N. Capitol St. N.W.
Washington, DC 20402
www.gpoaccess.gov/cfr/index.html
International Code Council (ICC)
500 New Jersey Avenue N.W.
6th Floor
Washington DC, 20001
www.iccsafe.org
International Concrete Repair Institute (ICRI)
3166 S. River Road Suite 132
Des Plains, IL 60018
www.icri.org
16.2—Cited references
AASHTO, 2004, “LRFD Bridge Design Specifications,”
Customary U.S. Units, third edition, Publication Code
LRFDUS-3, AASHTO, Washington, DC.
ACI Committee 318, 2005, “Building Code Requirements
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(318R-05),” American Concrete Institute, Farmington Hills,
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Aiello, M. A.; Galati, N.; and Tegola, L. A., 2001, “Bond
Analysis of Curved Structural Concrete Elements
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Concrete Structures (FRPRCS-5), Cambridge-Thomas
Telford, London, pp. 680-688.
Apicella, F., and Imbrogno, M., 1999, “Fire Performance
of CFRP-Composites Used for Repairing and Strengthening
Concrete,” Proceedings of the 5th ASCE Materials Engineering
Congress, Cincinnati, OH, May, pp. 260-266.
Arduini, M., and Nanni, A., 1997, “Behavior of Pre-Cracked
RC Beams Strengthened with Carbon FRP Sheets,” Journal
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Bank, L. C., 2006, Composites for Construction: Structural
Design with FRP Materials, John Wiley & Sons, Hoboken,
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Benmokrane, B., and Rahman, H., eds., 1998, Durability
of Fiber Reinforced Polymer (FRP) Composites for
Construction, University of Sherbrooke, Canada.
Bisby, L. A.; Green, M. F.; and Kodur, V. K. R., 2005a,
“Fire Endurance of Fiber-Reinforced Polymer-Confined
Concrete Columns,” ACI Structural Journal, V. 102, No. 6,
Nov.-Dec., pp. 883-891.
Bisby, L. A.; Green, M. F.; and Kodur, V. K. R., 2005b,
“Response to Fire of Concrete Structures that Incorporate
FRP,” Progress in Structural Engineering and Materials, V. 7,
No. 3, pp. 136-149.
Bousias, S.; Triantafillou, T.; Fardis, M.; Spathis, L.; and
O’Regan, B., 2004, “Fiber-Reinforced Polymer Retrofitting
of Rectangular Reinforced Concrete Columns with or
without Corrosion,” ACI Structural Journal, V. 101, No. 4,
July-Aug., pp. 512-520.
440.2R-68
ACI COMMITTEE REPORT
Bousselham, A., and Chaallal, O., 2006, “Behavior of
Reinforced Concrete T-Beams Strengthened in Shear with
Carbon Fiber-Reinforced Polymer—An Experimental
Study,” ACI Structural Journal, V. 103, No. 3, May-June,
pp. 339-347.
CALTRANS Division of Structures, 1996, Prequalification
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of Transportation, Sacramento, CA.
Carey, S. A., and Harries, K. A., 2005, “Axial Behavior
and Modeling of Small-, Medium-, and Large-Scale Circular
Sections Confined with CFRP Jackets,” ACI Structural
Journal, V. 102, No. 4, July-Aug., pp. 596-604.
Chaallal, O., and Shahawy, M., 2000, “Performance of
Fiber-Reinforced Polymer-Wrapped Reinforced Concrete
Column under Combined Axial-Flexural Loading,” ACI
Structural Journal, V. 97, No. 4, July-Aug., pp. 659-668.
Chajes, M.; Januska, T.; Mertz, D.; Thomson, T.; and
Finch, W., 1995, “Shear Strengthening of Reinforced
Concrete Beams Using Externally Applied Composite
Fabrics,” ACI Structural Journal, V. 92, No. 3, May-June,
pp. 295-303.
Christensen, J. B.; Gilstrap, J. M.; and Dolan, C. W., 1996,
“Composite Materials Reinforcement of Masonry Structures,”
Journal of Architectural Engineering, V. 2, No. 12, pp. 63-70.
Concrete Society, 2004, “Design Guidance for Strengthening
Concrete Structures Using Fibre Composite Materials,”
Technical Report No. 55 (TR55), second edition, Surrey,
128 pp.
De Lorenzis, L.; Lundgren, K.; and Rizzo, A., 2004,
“Anchorage Length of Near-Surface-Mounted FRP Bars for
Concrete Strengthening—Experimental Investigation and
Numerical Modeling,” ACI Structural Journal, V. 101, No. 2,
Mar.-Apr., pp. 269-278.
De Lorenzis, L., and Nanni, A., 2001b, “Characterization
of FRP Rods as Near Surface Mounted Reinforcement,”
Journal of Composites for Construction, ASCE, V. 5, No. 2,
pp. 114-121.
De Lorenzis, L., and Tepfers, R., 2003, “Comparative
Study of Models on Confinement of Concrete Cylinders with
Fiber-Reinforced Polymer Composites,” Journal of Composites
for Construction, ASCE, V. 7, No. 3, pp. 219-237.
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Reinforced Concrete T-Beams with Externally Bonded
Fiber-Reinforced Polymer Sheets,” ACI Structural Journal,
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Deniaud, C., and Cheng, J. J. R., 2003, “Reinforced
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Construction, ASCE, V. 7, No. 4, pp. 302-310.
Dolan, C. W.; Rizkalla, S. H.; and Nanni, A., eds, 1999,
Fourth International Symposium on Fiber Reinforced
Polymer Reinforcement for Reinforced Concrete Structures,
SP-188, American Concrete Institute, Farmington Hills, MI.
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Alternative Materials for the Reinforcement and
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Ehsani, M.; Saadatmanesh, H.; and Al-Saidy, A., 1997,
“Shear Behavior of URM Retrofitted with FRP Overlays,”
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El-Maaddawy, T.; Chahrour, A.; and Soudki, K. A., 2006,
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Elnabelsy, G., and Saatcioglu, M., 2004, “Seismic Retrofit
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DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
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440.2R-70
ACI COMMITTEE REPORT
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440.2R-71
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440.2R-72
ACI COMMITTEE REPORT
APPENDIX A—MATERIAL PROPERTIES OF
CARBON, GLASS, AND ARAMID FIBERS
Table A1.1 presents ranges of values for the tensile
properties of carbon, glass, and aramid fibers. The tabulated
values are based on the testing of impregnated fiber yarns or
strands in accordance with Suppliers of Advanced
Composite Materials Association Test Method 16-90. The
strands or fiber yarns are impregnated with resin, cured, and
then tested in tension. The tabulated properties are calculated
using the area of the fibers; the resin area is ignored. Hence,
the properties listed in Table A1.1 are representative of
unidirectional FRP systems whose properties are reported
using net-fiber area (Section 4.3.1).
Table A1.2 presents ranges of tensile properties for CFRP,
GFRP, and AFRP bars with fiber volumes of approximately
50 to 70%. Properties are based on gross-laminate area
(Section 4.3.1).
Table A1.3 presents ranges of tensile properties for CFRP,
GFRP, and AFRP laminates with fiber volumes of approximately 40 to 60%. Properties are based on gross-laminate
area (Section 4.3.1). The properties are shown for unidirectional, bidirectional, and +45/–45-degree fabrics. Table A1.3
also shows the effect of varying the fiber orientation on the
0-degree strength of the laminate.
Table A1.4 gives the tensile strengths of some commercially available FRP systems. The strength of unidirectional
laminates is dependent on fiber type and dry fabric weight.
These tables are not intended to provide ultimate strength
values for design purposes.
Table A1.1—Typical tensile properties of fibers used in FRP systems
Elastic modulus
Ultimate strength
3
10 ksi
GPa
ksi
MPa
Rupture strain,
minimum, %
General purpose
High-strength
32 to 34
32 to 34
220 to 240
220 to 240
300 to 550
550 to 700
2050 to 3790
3790 to 4820
1.2
1.4
Ultra-high-strength
High-modulus
32 to 34
50 to 75
220 to 240
340 to 520
700 to 900
250 to 450
4820 to 6200
1720 to 3100
1.5
0.5
Ultra-high-modulus
75 to 100
520 to 690
200 to 350
1380 to 2400
0.2
10 to 10.5
12.5 to 13
69 to 72
86 to 90
270 to 390
500 to 700
1860 to 2680
3440 to 4140
4.5
5.4
Fiber type
Carbon
Glass
E-glass
S-glass
Aramid
General purpose
10 to 12
69 to 83
500 to 600
3440 to 4140
2.5
High-performance
16 to 18
110 to 124
500 to 600
3440 to 4140
1.6
Table A1.2—Tensile properties of FRP bars with fiber volumes of 50 to 70%
FRP system description
High-strength carbon/epoxy
Young’s modulus,
103 ksi (GPa)
17 to 24 (115 to 165)
Ultimate tensile strength,
ksi (MPa)
180 to 400 (1240 to 2760)
Rupture strain, %
1.2 to 1.8
E-glass/epoxy
4 to 7 (27 to 48)
70 to 230 (480 to 1580)
1.6 to 3.0
High-performance aramid
8 to 11 (55 to 76)
130 to 280 (900 to 11,930)
2.0 to 3.0
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
440.2R-73
Table A1.3—Tensile properties of FRP laminates with fiber volumes of 40 to 60%
FRP system description
(fiber orientation)
Young’s modulus
Property at 0 degrees Property at 90 degrees
103 ksi (GPa)
Ultimate tensile strength
Property at 0 degrees
Property at 90 degrees
103 ksi (GPa)
ksi (MPa)
ksi (MPa)
Rupture strain
at 0 degrees, %
5 to 10 (35 to 70)
1.0 to 1.5
High-strength carbon/epoxy, degrees
0
15 to 21 (100 to 140)
0.3 to 1 (2 to 7)
150 to 350 (1020 to 2080)
0/90
8 to 11 (55 to 76)
8 to 11 (55 to 75)
100 to 150 (700 to 1020) 100 to 150 (700 to 1020)
+45/–45
2 to 4 (14 to 28)
2 to 4 (14 to 28)
25 to 40 (180 to 280)
E-glass/epoxy, degrees
0
3 to 6 (20 to 40)
0.3 to 1 (2 to 7)
75 to 200 (520 to 1400)
5 to 10 (35 to 70)
1.5 to 3.0
0/90
+45/–45
2 to 5 (14 to 34)
2 to 3 (14 to 21)
2 to 5 (14 to 35)
2 to 3 (14 to 20)
75 to 150 (520 to 1020)
25 to 40 (180 to 280)
75 to 150 (520 to 1020)
25 to 40 (180 to 280)
2.0 to 3.0
2.5 to 3.5
High-performance aramid/epoxy, degrees
0
7 to 10 (48 to 68)
0.3 to 1 (2 to 7)
100 to 250 (700 to 1720)
5 to 10 (35 to 70)
2.0 to 3.0
0/90
+45/–45
4 to 5 (28 to 34)
1 to 2 (7 to 14)
4 to 5 (28 to 35)
1 to 2 (7 to 14)
40 to 80 (280 to 550)
20 to 30 (140 to 210)
40 to 80 (280 to 550)
20 to 30 (140 to 210)
2.0 to 3.0
2.0 to 3.0
25 to 40 (180 to 280)
1.0 to 1.5
1.5 to 2.5
Notes:
FRP composite properties are based on FRP systems having an approximate fiber volume of 50% and a composite thickness of 0.1 in. (2.5 mm). In general, FRP bars have fiber
volumes of 50 to 70%, precured systems have fiber volumes of 40 to 60%, and wet layup systems have fiber volumes of 25 to 40%. Because the fiber volume influences the
gross-laminate properties, precured laminates usually have higher mechanical properties than laminates created using the wet layup technique.
Zero degrees represents unidirectional fiber orientation.
Zero/90 degrees (or +45/–45 degrees) represents fiber balanced in two orthogonal directions, where 0 degrees is the direction of loading, and 90 degrees is normal to the direction of
loading.
Tension is applied to 0-degree direction. All FRP bar properties are in the 0-degree direction.
Table A1.4—Ultimate tensile strength* of some commercially available FRP systems
Ultimate strength†
Fabric weight
g/m3
200
lb/in.
2600
kN/mm
500
12
400
3550
620
7
230
1800
320
High-strength carbon/resin unidirectional sheet
9
18
300
620
4000
5500
700
960
High-modulus carbon/resin unidirectional sheet
General-purpose carbon/resin balanced sheet
9
9
300
300
3400
1000
600
180
E-glass/resin unidirectional sheet
27
10
900
350
4100
1300
720
230
FRP system description (fiber type/saturating resin/fabric type)
General purpose carbon/resin unidirectional sheet
oz/yd3
6
E-glass/balanced fabric
Aramid/resin unidirectional sheet
9
300
680
120
12
420
4000
700
High-strength carbon/resin precured, unidirectional laminate
70‡
2380‡
19,000
3300
‡
‡
9000
1580
E-glass/vinyl ester precured, unidirectional shell
50
1700
*
Values shown should not be used for design.
Ultimate tensile strength per unit width of sheet or fabric.
‡
Precured laminate weight.
†
APPENDIX B—SUMMARY OF
STANDARD TEST METHODS
ACI 440.3R provides test methods for the short-term and
long-term mechanical and durability testing of FRP rods and
sheets. The recommended test methods are based on the
knowledge gained from research results and literature
worldwide. It is anticipated that these test methods may be
considered, modified, and adopted, either in whole or in part,
by a U.S. national standards-writing agency such as ASTM
or AASHTO. The publication of these test methods by ACI
Committee 440 is an effort to aid in this adoption.
ASTM test methods that quantify the structural behavior
of FRP systems bonded to concrete are in preparation.
Certain existing ASTM test methods are applicable to the
FRP material. FRP materials can be tested in accordance
with the methods listed in Table B1.1 as long as all exceptions
to the method are listed in the test report. Durability-related
tests use the same test methods but require applicationspecific preconditioning of specimens. Acceptance of the
data generated by the listed test methods can be the basis for
FRP material system qualification and acceptance.
440.2R-74
ACI COMMITTEE REPORT
Table B1.1—Test methods for FRP material systems
Property
ASTM test method(s)
Test methods for sheets, prepreg, and laminates
Surface hardness
D2538
D2240
ACI 440.3R test method
—
Summary of differences
No ACI methods developed.
D3418
Coefficient of thermal expansion
D696
—
No ACI methods developed.
Glass-transition temperature
D4065
D3171
—
No ACI methods developed.
—
No ACI methods developed.
Volume fraction
D2584
Sheet to concrete adhesion
(direct tension pull-off)
D4551
L.1
Tensile strength and modulus
D3039
L.2
Lap shear strength
D3165
D3528
ACI method provides specific requirements for specimen preparation
not found in the ASTM method
ACI method provides methods for calculating tensile strength and
modulus on gross cross-sectional and effective fiber area basis.
Section 3.3.1 of ACI 440.2R is used to calculate design values.
L.3
ACI method provides specific requirements for specimen preparation.
Test methods for FRP bars
Cross-sectional area
D7205
B.1
Two options for bar area are provided in D7205 (nominal and actual)
whereas only nominal area is used in 440.3R method B.1
Longitudinal tensile strength and
modulus
D7205
B.2
Strain limits for calculation of modulus are different in the two methods.
B.4
The ACI method focuses on dowel action of bars and does not overlap
with existing ASTM methods that focus mainly on beam shearing failure
modes. Bar shear strength is of specific concern for applications where
FRP rods are used to cross construction joints in concrete pavements.
No existing ASTM test methods available.
D5379/D5379M
Shear strength
D3846
D2344/D2344M
Durability properties
D4475
—
B.6
Fatigue properties
D3479/D3479M
B.7
Creep properties
D2990
B.8
Relaxation properties
Flexural tensile properties
Flexural properties
Coefficient of thermal expansion
Glass-transition temperature
Volume fraction
D2990
E328
B.9
—
D790
B.11
—
D4476
E831
—
D696
E1356
E1640
D648
E2092
D3171
ACI methods provide specific information on anchoring bars in the test
fixtures and on attaching elongation measuring devices to the bar. The
ACI methods also require specific calculations that are not provided in
the ASTM methods.
No existing ASTM test methods available.
No ACI methods developed.
—
No ACI methods developed.
—
No ACI methods developed.
—
No ACI methods developed.
APPENDIX C—AREAS OF FUTURE RESEARCH
As mentioned in the body of the document, future research
is needed to provide information in areas that are still unclear
or are in need of additional evidence to validate performance. The list of topics presented in this appendix provides
a summary.
Materials
• Confirmation of normal (Gaussian) distribution representing the tensile strength of a population of FRP
strengthening systems;
• Methods of fireproofing FRP strengthening systems;
• Behavior of FRP-strengthened members under elevated
temperatures;
• Behavior of FRP-strengthened members under cold
temperatures;
• Fire rating of concrete members strengthened with
FRP bars;
•
Effect of different coefficients of thermal expansion
between FRP systems and member substrates;
• Creep-rupture behavior and endurance times of FRP
systems; and
• Strength and stiffness degradation of FRP systems in
harsh environments.
Flexure/axial force
• Compression behavior of noncircular members
wrapped with FRP systems;
• Behavior of members strengthened with FRP
systems oriented in the direction of the applied axial
load;
• Effects of high concrete strength on behavior of FRPstrengthened members;
• Effects of lightweight concrete on behavior of FRPstrengthened members;
DESIGN AND CONSTRUCTION OF EXTERNALLY BONDED FRP SYSTEMS
440.2R-75
•
Maximum crack width and deflection prediction and
control of concrete reinforced with FRP systems; and
• Long-term deflection behavior of concrete flexural
members strengthened with FRP systems.
Shear
• Effective strain of FRP systems that do not completely
wrap around the section; and
• Use of FRP systems for punching shear reinforcement
in two-way systems.
Detailing
• Anchoring of FRP systems.
The design guide specifically indicated that test methods
are needed to determine the following properties of FRP:
• Bond characteristics and related bond-dependent
coefficients;
• Creep-rupture and endurance times;
• Fatigue characteristics;
• Coefficient of thermal expansion;
• Shear strength; and
• Compressive strength.
APPENDIX D—METHODOLOGY FOR
COMPUTATION OF SIMPLIFIED P-M INTERACTION
DIAGRAM FOR NONCIRCULAR COLUMNS
P-M diagrams may be developed by satisfying strain
compatibility and force equilibrium using the model for the
stress strain behavior for FRP-confined concrete presented
in Eq. (12-2). For simplicity, the portion of the unconfined
and confined P-M diagrams corresponding to compressioncontrolled failure can be reduced to two bilinear curves
passing through the following three points (Fig D.1). (The
following only makes reference to the confined case because
the unconfined one is analogous):
• Point A (pure compression) at a uniform axial compressive strain of confined concrete εccu;
• Point B with a strain distribution corresponding to zero
strain at the layer of longitudinal steel reinforcement
nearest to the tensile face, and a compressive strain εccu
on the compression face; and
• Point C with a strain distribution corresponding to
balanced failure with a maximum compressive strain εccu
and a yielding tensile strain εsy at the layer of longitudinal steel reinforcement nearest to the tensile face.
For confined concrete, the value of φPn corresponding to
Point A (φMn equals zero) is given in Eq. (12-1), while the
coordinates of Points B and C can be computed as:
φP n ( B, C ) = φ [ ( A ( y t ) + B ( y t ) + C ( y t ) + D ) + ∑ A si f si ]
3
2
(D-1)
φM n ( B, C ) = φ [ ( E ( y t ) + F ( y t ) + G ( y t ) + H ( y t ) + I ) + ∑ A si f sid i] (D-2)
4
3
2
Fig. D.1—Strain distributions for Points B and C for simplified
interaction diagram.
b ( E c – E 2 ) ⎛ ε ccu⎞
B = --------------------------------⎝ c ⎠
2
(D-3b)
C = –bfc′
(D-3c)
bcE
D = bcf c′ + -----------2- ( ε ccu )
2
(D-3d)
2
– b ( E c – E 2 ) ⎛ ε ccu⎞ 2
E = ------------------------------ --------⎝ c ⎠
16f c′
(D-3e)
2
( E c – E 2 ) ⎛ ε ccu⎞ 2 b ( E c – E 2 ) ⎛ ε ccu⎞
F = b ⎛ c – h---⎞ -------------------------------- + ------------------------- --------- (D-3f)
⎝
⎝ c ⎠
2⎠ 12f c ′ ⎝ c ⎠
3
( E c – E 2 ) ⎛ ε ccu⎞ ⎞
G = ⎛ b--- f c′ + b ⎛ c – h---⎞ --------------------- --------⎝
⎝2
⎝ c ⎠⎠
2⎠
2
(D-3g)
h
H = bf c′ ⎛ c – ---⎞
⎝
2⎠
(D-3h)
2
2
bcE
bc E
h
h
I = bc
-------- f c′ – bcf c′ ⎛ c – ---⎞ + --------------2 ( ε ccu ) – ------------2 ⎛ c – ---⎞ ( ε ccu )
⎝
h
3
2 ⎝
2⎠
2⎠
(D-3i)
where
2
– b ( E c – E 2 ) ⎛ ε ccu⎞ 2
A = ------------------------------ --------⎝ c ⎠
12f c′
(D-3a)
In Eq. (D-3), c is the distance from the extreme compression
fiber to the neutral axis (Fig D.1) and it is given by Eq. (D-4).
The parameter yt represents the vertical coordinate within the
compression region measured from the neutral axis position
440.2R-76
ACI COMMITTEE REPORT
Fig. D.2—Flowchart for application of methodology.
(Fig. D.1) and corresponds to the transition strain εt′ (Eq. (D-5)
[see Fig. D.1]).
⎧d
⎪
c = ⎨
ε ccu
⎪ d --------------------⎩ ε sy + ε ccu
for Point B
for Point C
ε t′
y t = c -------ε ccu
(D-4)
(D-5)
in which fsi is the stress in the i-th layer of longitudinal steel
reinforcement. The values are calculated by similar triangles
from the strain distribution corresponding to Points B and C.
Depending on the neutral axis position c, the sign of fsi will
be positive for compression and negative for tension. A
flowchart illustrating the application of the proposed
methodology is shown in Fig. D.2.
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Guide for the Design and Construction of Externally
Bonded FRP Systems for Strengthening Concrete Structures
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